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

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Answer 1 · 2018-06-29T13:02:29

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

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

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]

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