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 $f(x) = x^2e^{3x}$

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 $f(x) = x^3e^x$