Question

Differitiate:Y=X^2(X^2+2)^2

Answer 1

Let us differentiate using:

1. The Leibniz rule: if$f(x) = g_1(x) g_2(x) ... g_n(x)$, then $f'(x) = g_1' g_2 ... g_n + ... + g_1 ... g_n'$
2. The chain rule: if$f(x) = g(h(x))$ , then $f'(x) = g'(h(x))h'(x)$

Hence, $y'(x) = 2 x (x^2 + 2)^2 + x^2 \cdot 2 (x^2 + 2) \cdot 2 x = 2 (3 x^5 + 8 x^3 + 4 x)$.