While $f^{\prime }(x)$ could be computed using the product, quotient, and general power rules of differentiation, since there are more than two factors, each with an exponent, it is a good candidate for logarithmic differentiation.

Take the natural logarithm of both sides of $y=f(x)$ and expand $\ln (f(x))$ using laws of logarithms.

Recall ${\displaystyle \frac{d}{dx}}\ln (y)={\displaystyle \frac{y^{\prime }}{y}}$.

Multiply both sides by $y$ and replace $y$ with $f(x)$:

Observe that $f(x)$ is a function of $x$ (i.e., $3x+5$) raised to another function of $x$ (i.e., $x^2$). Logarithmic differentiation is the only technique of differentiation that can be applied to functions of the form $h(x{)}^{g(x)}$, as is the case here.

Take the natural logarithm of both sides of $y=f(x)$ and expand $\ln (f(x))$ using laws of logarithms.

Recall ${\displaystyle \frac{d}{dx}}\ln (f(x))={\displaystyle \frac{1}{f(x)}}{f}^{\prime }(x)$.

Multiply both sides by $y$ and replace $y$ with $f(x)$: