Question Type 5: Applying both chain rule and product rule together on composite functions Exercises

Differentiate $f(x)=x^3\ln(e^{2x}+3)$

Differentiate $f(x)=\tan(e^{3x})\,x$

Differentiate $f(x)=\sin(e^x+x^2)\;\ln(x^2+1)$. [4 marks]

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

Differentiate $f(x)=(e^{x^2}+1)(x^3+\sin x)$

Differentiate $f(x)=\cos(3x^2)\,\sqrt{x^2+4}$

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

Differentiate $f(x)=x\sqrt{e^{2x}+1}$.

Differentiate $f(x) = x^4 \ln(\sin(x^2))$ with respect to $x$.

Differentiate $f(x)=(x^2+1)e^{x^2}$. [3 marks]

Differentiate $f(x)=e^x(x^2+1)^5$, giving your answer in a fully factorized form. [4 marks]

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