Question

Differentiate f (x) = (8x^3 +4x)(2x^2 +5) using product rule

Differentiate (x^5 +6)^5 using chain rule

Answer 1

$1.f(x)=(8x^3+4x)(2x^2+5)$

$f'(x)=(24x^2+4)(2x^2+5)+4x(8x^3+4x)=48x^4+120x^2+8x^2+20+32x^4+16x^2=80x^4+144x^2+20$

$2.f(x)=(x^5+6)^5$

$f'(x)=5(x^5+6)^4(5x^4)=25x^4(x^5+6)^4$