find the derivative of y with respect to x.\n\n$y = \\ln(x^{10})$

Explanation:

Step1: Use the logarithmic property

We know that $\ln(a^b)=b\ln(a)$. So, $y = \ln(x^{10})=10\ln(x)$.

Step2: Differentiate using the formula for derivative of $\ln(x)$

The derivative of $\ln(x)$ with respect to $x$ is $\frac{1}{x}$. Using the constant - multiple rule $(cf(x))^\prime = cf^\prime(x)$ (where $c = 10$ and $f(x)=\ln(x)$), we get $\frac{dy}{dx}=10\times\frac{1}{x}$.

Answer:

$\frac{10}{x}$