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

1 Answer
Mar 5, 2016

#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.