Question Type 1: Calculating derivatives of complicated functions Exercises

Differentiate $f(x) = x^2 e^{-x}$.

Differentiate $f(x) = \ln(\sin x)$.

Differentiate $f(x) = \sin^2 x \, e^x$.

Differentiate $f(x) = e^{2x}$.

Differentiate $f(x) = \arctan(x^3)$.

Differentiate $f(x)=e^{2x}\sin(3x)$.

Differentiate $f(x) = \frac{\ln x}{x^2}$

Differentiate $f(x) = 3^x \ln x$.

Find $f'(x)$ for $f(x) = \frac{4x^{-3}}{9} + 3\ln x - \sin x$.

Differentiate $f(x) = \ln(x^2 + 1)$.

Differentiate $f(x) = x^x$

Differentiate $f(x) = \frac{e^{3x}}{x}$.