Question

How do you find the derivative of `6x^(- 7/8)`?

Answer 1

`f'(x)=-21/4x^(-15/8)`

Explanation:

Before we derive this, we shall first remind ourselves of 2 important formulas, `f(x)=kh(x)\impliesf'(x)=kh'(x)` and `f(x)=x^n\impliesf'(x)=nx^(n-1)`

Now, we have `f(x)=6x^(-7/8)`
From above equations, we take `k=6` and `g(x)=x^(-7/8)`
So, `f'(x)=6*(d(x^(-7/8)))/dx\impliesf'(x)=-6*7/8*x^(-15/8)`

Simplifying gives us the answer.