IB Mathematics Analysis and Approaches Question Type 1: Calculating the Second Derivatives of Functions Involving Less Rules Exercises

Calculate the second derivative of $f(x)=\ln (x^2+1)$

Calculate the second derivative of $f(x)=x{e}^{2x}$

Calculate the second derivative of $f(x)=\sin (x^2)$ [4 marks]

Calculate the second derivative of $f(x)=e^x\cos x$

Calculate the second derivative of $f(x)=x^4+5x^2-3x+7$ [2 marks]

Calculate the second derivative of $f(x)=x^2{e}^{3x}$

Calculate the second derivative of $f(x)={\tan }^{-1}(x)$

Calculate the second derivative of $f(x)=e^{x^2}$

Calculate the second derivative of $f(x)=(3x+4{)}^5$

Calculate the second derivative of $f(x)=(x^2+2{)}^2+e^{2x}$

Calculate the second derivative of $f(x)=\ln (\sin x)$.

Calculate the second derivative of $f(x)=x^3{e}^x$