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

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

1 Answer
Jan 20, 2018

f'(3)=525/8

f'(-2)=50/3

Explanation:

We want to find the derivative of:

f(x)=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^2+5/8x^4

f'(x)=5/3x^2+5/8x^4

Therefore:

f'(3)=5/3*3^2+5/8*3^4=120/8+405/8=525/8

And

f'(-2)=5/3(-2)^2+5/8(-2)^4=20/3+80/8=50/3