`f(x) = 2/(root(3)(x)) + 3cos(x)` Find the derivative of the function.

1 Answer

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kalau | (Level 2) Adjunct Educator

Posted on

The first term is the same as:

`2/x^(1/3) =2x^(-1/3)`

Take the derivative of this term.

`-1/3(2)x^(-1/3-1) = -2/3x^(-4/3)`

The derivative of `3cos(x)` is `-3sin(x)` .  

Combine the terms.

`f'(x)=-2/3x^(-4/3)-3sin(x)` 

Rewrite the first term to eliminate the negative exponent.

The answer is:

`f'(x)=-2/(3x^(4/3))-3sin(x)`