IB Mathematics Analysis and Approaches Question Type 2: Calculating the Second Derivatives of Much More Complicated Functions Exercises

Find $f^{\prime \prime }(x)$ for $f(x)=e^{2x}\sin (3x)$.

Determine the second derivative of $f(x)=e^{x^2}\cos x$.

Calculate $f^{\prime \prime }(x)$ for $f(x)=x\ln (x)e^{-x}$.

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

Find the second derivative of $f(x)=\arctan (e^x)$. [6]

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

Find $f^{\prime \prime }(x)$ for $f(x)=x^x$.

Determine the second derivative of $f(x)=\frac{\sin (\ln x)}{x}$.