Question Type 2: Calculating the second derivatives of much more complicated functions Exercises

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

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

Calculate $f''(x)$ 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 $f(x)=x^3e^x$.

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

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