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What is the derivative of #(x^3 + 2)^2(x^5 + 4)^4#?

1 Answer

Jun 29, 2018

# f^'(x) =2 x^2(x^3+2)(x^5+4)^3 ( 13 x ^5+20 x^2+12)#

Explanation:

#f(x) = (x^3+2)^2 (x^5+4)^4#

Product rule : #d/d x (f g)= f g^'+g f^'#

#f^'(x) = (x^3+2)^2 * 4 (x^5+4)^3 * (5 x^4) +(x^5+4)^4 * 2(x^3+2)*(3 x^2)#

#f^'(x) =2 x^2(x^3+2)(x^5+4)^3 {( 10 x^5+20x^2)+(3 x^5+12)}#

# f^'(x) =2 x^2(x^3+2)(x^5+4)^3 ( 13 x ^5+20 x^2+12)# [Ans]

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