R S Aggarwal Solutions for Exercise 10: EXERCISE

Find the second derivative of $5^x$

Find the second derivative of ${\cos }^{-1}x$

Find the second derivative of $e^{2x}\cos 3x$

If the second derivative of $x^3\log x$ is $x\left(m+n\log x\right)$, then find the value of $m+n$.

Find the second derivative of $e^{3x}\sin 4x$.

Find the second derivative of $\sin 3x\cos 5x$.

If $x=a{t}^2$ and  $y= 2at$, find $\frac{d^{2}y}{d{x}^2}$ at $t= 2$.

If $x=a(\theta -\sin \theta )$ and $y= a(1 – \cos \theta )$, find $\frac{d^{2}y}{d{x}^2}$ at $\theta =\pi$