Question

Let f(x)= (5)/(9x^3)+(1)/(8x^5) evaluate?

f'(3)=?
f'(-2)=?

Answer 1

`f'(3)=-125/5832`

`f'(-2)=-175/1536`

Explanation:

We want to find the derivative of:

`f(x)=5/(9x^3)+1/(8x^5)=5/9x^-3+1/8x^-5`

Use the power rule for derivatives:

If `f(x)=x^n` then `f'(x)=nx^(n-1)`

Apply the rule:

`f'(x)=(-3)*5/9x^(-3-1)+(-5)1/8x^(-5-1)`

`f'(x)=-15/9x^-4-5/8x^-6`

`f'(x)=-5/(3x^4)-5/(8x^6)`

Therefore:

`f'(3)=-5/(3*3^4)-5/(8*3^6)=-5/243-5/5832=-125/5832`

And

`f'(-2)=-5/(3*(-2)^4)-5/(8*(-2)^6)=-5/48-5/512=-175/1536`