Math at eNotes
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The latest questions and answers, from members following Math at eNotes.Tue, 6 Oct 2015 20:47:39 PSTen-usNote:- 1) If y = cosx; then dy/dx = -sinx 2) If y = x^n ; then dy/dx =...
http://www.enotes.com/homework-help/f-x-xcos-x-c-pi-4-find-f-x-f-c-521125
Note:- 1) If y = cosx; then dy/dx = -sinx 2) If y = x^n ; then dy/dx = n*x^(n-1) 3) If y = u*v ; where u & v are functions of 'x'; then dy/dx = uv' + vu' Now, `f(x) = xcos(x)` `f'(x) = -xsin(x) + cos(x)` `f'(c) = f'(pi/4) = -(pi/4)*sin(pi/4) + cos(pi/4) ` `or, f'(pi/4) = 0.152` ``http://www.enotes.com/homework-help/f-x-xcos-x-c-pi-4-find-f-x-f-c-521125Tue, 6 Oct 2015 20:47:39 PSTFind the derivative of `h(x)=(8)/(5x^4)` First rewrite the function as...
http://www.enotes.com/homework-help/h-x-8-5x-4-use-rules-differentiation-find-521302
Find the derivative of `h(x)=(8)/(5x^4)` First rewrite the function as `h(x)=(8x^-4)/(5)` then find the derivative of the function using the power rule. `h'(x)=(-4)(8/5)x^-5` The derivative is: `h'(x)=-32/(5x^5)` ``http://www.enotes.com/homework-help/h-x-8-5x-4-use-rules-differentiation-find-521302Tue, 6 Oct 2015 20:46:35 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/y-sin-x-x-4-use-product-rule-quotient-rule-find-521318
You need to evaluate the derivative of the given function and since the function is a quotient of two functions, then you must use the quotient rule, such that: `f'(x) = ((x^4)(sin x)' - (x^4)'(sin x))/(x^8)` `f'(x) = (x^4*cos x - 4x^3*sin x)/(x^8)` Factoring out `x^3 ` yields: `f'(x) = x^3(x*cos x - 4*sin x)/(x^8)` Reducing like terms yields: `f'(x) = (x*cos x - 4*sin x)/(x^5)` Hence, evaluating the derivative of the function, using the...http://www.enotes.com/homework-help/y-sin-x-x-4-use-product-rule-quotient-rule-find-521318Tue, 6 Oct 2015 20:44:25 PSTNote:- If y = x^n ; where n = constant ; then dy/dx = n*x^(n-1) Now,...
http://www.enotes.com/homework-help/h-s-s-3-2-2-find-derivative-algebraic-function-521133
Note:- If y = x^n ; where n = constant ; then dy/dx = n*x^(n-1) Now, `h(s) = (s^3 - 2)^2` `h'(s) = (3s^2)*(s^3-2)^1` `or, h'(s) = (3s^2)*(s^3 - 2)` `or, h'(s) = 3s^5 - 6s^2` `` ` `http://www.enotes.com/homework-help/h-s-s-3-2-2-find-derivative-algebraic-function-521133Tue, 6 Oct 2015 20:43:43 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/y-x-4-cos-x-use-product-rule-quotient-rule-find-521317
You need to evaluate the derivative of the given function and since the function is a quotient of two functions, then you must use the quotient rule, such that: `f'(x) = ((x^4)'(cos x) - (x^4)(cos x)')/((cos x)^2)` `f'(x) = (4x^3*cos x + x^4*sin x)/((cos x)^2)` Factoring out `x^3` yields: `f'(x) = x^3(4x*cos x + x*sin x)/((cos x)^2)` Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = x^3(4x*cos x + x*sin...http://www.enotes.com/homework-help/y-x-4-cos-x-use-product-rule-quotient-rule-find-521317Tue, 6 Oct 2015 20:41:33 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/f-x-2x-7-x-2-4-use-product-rule-quotient-rule-521316
You need to evaluate the derivative of the given function and since the function is a quotient of two polynomials, then you must use the quotient rule, such that: `f'(x) = ((2x+7)'(x^2+4) - (2x+7)(x^2+4)')/((x^2+4)^2)` `f'(x) = (2(x^2+4) - (2x+7)(2x))/((x^2+4)^2)` `f'(x) = (2x^2 + 8 - 4x^2 - 14x)/((x^2+4)^2)` Combining like terms yields: `f'(x) = (-2x^2 - 14x + 8)/((x^2+4)^2)` Hence, evaluating the derivative of the function, using the product...http://www.enotes.com/homework-help/f-x-2x-7-x-2-4-use-product-rule-quotient-rule-521316Tue, 6 Oct 2015 20:39:05 PSTIn order to find the slope of a function at a specific point, first find...
http://www.enotes.com/homework-help/f-x-2x-4-8-0-8-find-slope-graph-functions-given-521309
In order to find the slope of a function at a specific point, first find the derivative of the function, then plug in the x-value from the given point. Given: `f(x)=2x^4-8, (0,-8)` `f'(x)=8x` `f'(0)=8(0)` `f'(0)=0` The slope is 0.http://www.enotes.com/homework-help/f-x-2x-4-8-0-8-find-slope-graph-functions-given-521309Tue, 6 Oct 2015 20:38:27 PSTNote:- 1) If y = secx ; then dy/dx = sec(x)*tan(x) 2) If y = x^n ; where...
http://www.enotes.com/homework-help/h-x-1-x-12sec-x-find-derivative-trigonometric-521148
Note:- 1) If y = secx ; then dy/dx = sec(x)*tan(x) 2) If y = x^n ; where n = constant ; then dy/dx = n*x^(n-1) Now, `y = 1/x - 12sec(x)` `y' = dy/dx = -1/x^2 - 12sec(x)*tan(x)` ``http://www.enotes.com/homework-help/h-x-1-x-12sec-x-find-derivative-trigonometric-521148Tue, 6 Oct 2015 20:36:44 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/f-x-x-2-x-1-x-2-1-use-product-rule-quotient-rule-521315
You need to evaluate the derivative of the given function and since the function is a quotient of two polynomials, then you must use the quotient rule, such that: `f'(x) = ((x^2+x-1)'(x^2-1) - (x^2+x-1)(x^2-1)')/((x^2-1)^2)` `f'(x) = ((2x+1)(x^2-1) - (x^2+x-1)(2x))/((x^2-1)^2)` `f'(x) = (2x^3 - 2x + x^2 - 1 - 2x^3 - 2x^2 + 2x)/((x^2-1)^2)` Reducing like terms yields: `f'(x) = (-x^2 - 1)/((x^2-1)^2)` Hence, evaluating the derivative of the...http://www.enotes.com/homework-help/f-x-x-2-x-1-x-2-1-use-product-rule-quotient-rule-521315Tue, 6 Oct 2015 20:35:58 PSTIn order to find the slope of a function at a given point, find the...
http://www.enotes.com/homework-help/f-x-3x-2-4x-1-1-find-slope-graph-functions-given-521308
In order to find the slope of a function at a given point, find the derivative of the function then plug in the x-value. Given: `f(x)=3x^2-4x, (1, -1)` `f'(x)=6x` `f'(1)=6(1)` `f'(1)=6` ``http://www.enotes.com/homework-help/f-x-3x-2-4x-1-1-find-slope-graph-functions-given-521308Tue, 6 Oct 2015 20:34:40 PSTNote:- 1) If y = tanx ; then dy/dx = sec^2(x) 2) If y = x^n ; where 'n'...
http://www.enotes.com/homework-help/f-x-x-2-tan-x-find-derivative-trigonometric-521153
Note:- 1) If y = tanx ; then dy/dx = sec^2(x) 2) If y = x^n ; where 'n' = constant ; then dy/dx = n*x^(n-1) 3) If y = u*v ; where 'u' & 'v' are functions of 'x', then dy/dx = uv' + vu' Now, `f(x) = (x^2)tanx` `f'(x) = 2x*tanx + (x^2)sec^2(x)` `or, f'(x) = x[2tanx + (x^2)sec^2x]` ``http://www.enotes.com/homework-help/f-x-x-2-tan-x-find-derivative-trigonometric-521153Tue, 6 Oct 2015 20:32:45 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/f-t-2-t-5-cos-t-use-product-rule-quotient-rule-521314
You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that: `f'(t) = (2t^5)'(cos t) + (2t^5)(cos t)'` `f'(t) = (10t^4)(cos t) + (2t^5)(-sin t)` Hence, evaluating the derivative of the function, using the product rule, yields` f'(t) = (10t^4)(cos t) - (2t^5)(sin t).`http://www.enotes.com/homework-help/f-t-2-t-5-cos-t-use-product-rule-quotient-rule-521314Tue, 6 Oct 2015 20:30:57 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/h-x-sqrt-x-sin-x-use-product-rule-quotient-rule-521313
You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that: `f'(x) = (sqrt x)'(sin x) + (sqrt x)(sin x)'` `f'(x) = (1/(2sqrt x))(sin x) + (sqrt x)(cos x)` Hence, evaluating the derivative of the function, using the product rule, yields `f'(x) = (1/(2sqrt x))(sin x) + (sqrt x)(cos x).`http://www.enotes.com/homework-help/h-x-sqrt-x-sin-x-use-product-rule-quotient-rule-521313Tue, 6 Oct 2015 20:28:50 PSTNote:- 1) If y = secx ; then dy/dx = secx*tanx 2) If y = x^n ; then...
http://www.enotes.com/homework-help/y-sec-x-x-find-derivative-trigonometric-function-521150
Note:- 1) If y = secx ; then dy/dx = secx*tanx 2) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = constant 3) If y = u/v ; where 'u' & 'v' are functions of 'x' , then dy/dx = [vu'-uv']/(v^2) Now, `y = sec(x)/x` `dy/dx = y' = [x*sec(x)*tan(x) - sec(x)]/x^2` `or, y' = dy/dx = sec(x)*[xtan(x)-1]/(x^2)` ``http://www.enotes.com/homework-help/y-sec-x-x-find-derivative-trigonometric-function-521150Tue, 6 Oct 2015 20:28:20 PSTYou need to evaluate the derivative of the given function and since the...
http://www.enotes.com/homework-help/g-x-2x-3-5x-3x-4-use-product-rule-quotient-rule-521312
You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that: `f'(x) = (2x^3 + 5x)'(3x-4) + (2x^3 + 5x)(3x-4)'` `f'(x) = (6x^2 + 5)(3x-4) + (2x^3 + 5x)(3 - 0)` `f'(x) = 18x^3 - 24x^2 + 15x - 20 + 6x^3 + 15x` Combining like terms yields: `f'(x) = 24x^3 - 24x^2 + 30x - 20` Hence, evaluating the derivative of the function, using the product rule,...http://www.enotes.com/homework-help/g-x-2x-3-5x-3x-4-use-product-rule-quotient-rule-521312Tue, 6 Oct 2015 20:25:59 PST