Derivative Question.  If f(x)= −5x^5−3x^4−7x^3             ---------------------                     x^4 find f′(x). 

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aruv | High School Teacher | (Level 2) Valedictorian

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`f(x)=(-5x^5-3x^4-7x^3)/x^4`

`=(-x^3(5x^2+3x+7))/x^4`

`=-(5x^2+3x+7)x^3xxx^(-4)`

`=-(5x^2+3x+7)x^(-1)`

`=-5x-3-7x^(-1)`

`Thus`

`f'(x)=-5-7(-1)x^(-2)`

`=-5+7/x^2`

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The derivative of f(x)= (-5x^5-3x^4-7x^3)/x^4 is required.

f(x)= (-5x^5-3x^4-7x^3)/x^4

= (-5x^5)/x^4-(3x^4)/x^4-(7x^3)/x^4

= -5x - 3 - 7/x

= -5x^1 - 3*x^0 - 7*x^-1

If f(x) = x^n. f'(x) = n*x^(n-1).

This gives:

f'(x) = -5 - 0 + 7/x^2

The derivative of f(x)= (-5x^5-3x^4-7x^3)/x^4 is f'(x) = -5 + 7/x^2

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