Calculate y'. $y=4 \ln \left(x^{2} e^{x}\right)$
A) $y^{\prime}=4\left(\frac{2}{x}+1\right)$
B) $y^{\prime}=x \ln 2 x+x^{2}$
C) $y^{\prime}=4\left(\frac{2}{x}+2\right)$
D) $y^{\prime}=\frac{2 e^{x}+x \ln x^{2}}{x}$
E) $y^{\prime}=3 x^{2}$

Question

Quizplus · Accepted Answer

The derivative of $y = 4 \ln(x^2 e^x)$ is found using the chain rule and properties of logarithms: $y = 4(\ln(x^2) + \ln(e^x)) = 4(2\ln(x) + x)$. Differentiating gives $y' = 4(\frac{2}{x} + 1)$.

Calculate Y y=4ln⁡(x2ex)y=4 \ln \left(x^{2} e^{x}\right)y=4ln(x2ex) A) y′=4(2x+1)y^{\prime}=4\left(\frac{2}{x}+1\right)y′=4(x2​+1) B) y′=xln⁡2x+x2y^{\prime}=x \ln 2 x+x^{2}y′=xln2x+x2

Calculate Y $y=4 \ln \left(x^{2} e^{x}\right)$ A) $y^{\prime}=4\left(\frac{2}{x}+1\right)$ B) $y^{\prime}=x \ln 2 x+x^{2}$