IB Mathematics Analysis and Approaches 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 $f(x)=x{e}^{\sin (x^3)}$