find $\frac{dy}{du}$, $\frac{du}{dx}$, and $\frac{dy}{dx}$. $y = u^{55}… | Sovi AI

QUESTION IMAGE

$find $\frac{dy}{du}$, $\frac{du}{dx}$, and $\frac{dy}{dx}$. $y = u^{55}…$

Question

find $\frac{dy}{du}$, $\frac{du}{dx}$, and $\frac{dy}{dx}$. $y = u^{55}$ and $u = 2x^3 - 4x^2$ $\frac{dy}{du} = square$

Explanation:

Step1: Differentiate y with respect to u

Given \( y = u^{55} \), use the power rule \(\frac{d}{du}(u^n)=nu^{n - 1}\). Here \( n = 55 \), so \(\frac{dy}{du}=55u^{55 - 1}=55u^{54}\).

Answer:

\( 55u^{54} \)