differentiate the function. y = 6e^x + 4 / (∛x) y =

Explanation:

Step1: Recall derivative rules

The derivative of $e^x$ is $e^x$, and for $x^n$ the derivative is $nx^{n - 1}$. Rewrite $\frac{4}{\sqrt[3]{x}}$ as $4x^{-\frac{1}{3}}$.

Step2: Differentiate term - by - term

The derivative of $6e^x$ is $6e^x$ (since the derivative of $e^x$ is $e^x$ and the constant multiple rule: $(cf(x))'=cf'(x)$). The derivative of $4x^{-\frac{1}{3}}$ is $4\times(-\frac{1}{3})x^{-\frac{1}{3}-1}=-\frac{4}{3}x^{-\frac{4}{3}}$.

Answer:

$6e^x-\frac{4}{3}x^{-\frac{4}{3}}$