Calculate the derivative of the function f(x)=(sin x + cos x)/(2sin x - 3 cosx).
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to use the quotient rule to find the derivative of `f(x)=(sin x + cos x)/(2sin x - 3 cosx).`
Differentiating with respect to x yields:
`f'(x) = ((sin x + cos x)'*(2sin x - 3 cosx) - (sin x + cos x)*(2sin x - 3 cosx)')/(2sin x -...
(The entire section contains 155 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- `sin^(1/2)x cosx - sin^(5/2)x cosx = cos^3(x)sqrt(sin(x))` Verify the identity.
- 1 Educator Answer
- Solve for x: √3 sin x + cosx = 1
- 1 Educator Answer
- Calculate the indefinite integral of y = cos x / (sin x)^3.
- 1 Educator Answer
- `f(x) = 2sin(x) + cos(2x), [0, 2pi]` Find all relative extrema, use the second derivative...
- 1 Educator Answer
- `f(x) = sin(x) + cos(x)` Consider the function on the interval (0, 2pi). Find the open...
- 2 Educator Answers
istetz,
in the chain rule, the derivative of the function f(x)/g(x) is
{f'(x)*g(x) - f(x)*g'(x)}/[{g(x)}^2]
So, if we derive f(x) = (sinx + cosx)/(2sinx + 3cosx),
f'(x) =
{(cosx-sinx)*(2sinx-3cosx)-(sinx+cosx)*(2cosx+3sinx)}/{(2sinx - 3sinx)^2}
= -3(cosx)^2 - 2(sinx)^2 - 3(sinx)^2 -2(cosx)^2
Since (sinx)^2 + (cosx)^2 = 1,
the value of the equation above is
-3 -2 = -5
Hence, the derivative of f(x) is -5
Student Answers