Answer to Question #132343 in Calculus for Timmy

Question

Differentiate f(x) = (8x3 + 4x )(2x2 +5) using product rule.

Answer 1

$$Solution$$

$f(x)=h(x) \cdot g(x)\\ f'(x)=h'(x) \cdot g(x)+h(x) \cdot g'(x)\\ f(x)=(8x^3+4x)(2x^2+5)\\ f'(x)=(24x^2+4)(2x^2+5)+(8x^3+4x)(4x)\\ Expanding\\ =48x^4+120x^2+8x^2+20+32x^4+16x^2\\ \implies f'(x)=80x^4+144x^2+20-------->Answer$