Answer to Question #320374 in Calculus for koi

Question

Find 𝑑𝑦 𝑑𝑥 if 𝑦 = 𝑢 3 − 3𝑢 2 + 1 and 𝑢 = 𝑥 2 + 2 

Answer 1

$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}=\left( 3u^2-6u \right) \cdot 2x=6x\left( \left( x^2+2 \right) ^2-2\left( x^2+2 \right) \right) =\\=6x\left( x^4+2x^2 \right)$