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

Question

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

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Answer 1 · 2018-01-20T17:44:17

#f'(3)=525/8#

#f'(-2)=50/3#

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#