Differentiation

If $y=x^{2}+3x+2$ then find the slope of the tangent at point (0, 2).

Derivative of ${\left( \sqrt{x}+\dfrac{1}{\sqrt{x}} \right)}^{2}$ is

The distance ' $s$ ' in meters covered by a body in $t$ seconds is given by $s=3 t^{2}-8 t+5$. The body will stop after

$e^{e^{x}}$

If $y=e^{mx}+e^{-mx}$, then $\dfrac{d^{2}y}{dx^{2}}=$

If $f(x)=x\sin x$, then $f^{'}\left( \dfrac{\pi}{2} \right)$ is equal to

If $y=\sin \left(e^{\log 2 x}\right)$, then the value of $\dfrac{d y}{d x}$ at $x=\dfrac{\pi}{2}$ is

If $f(x)=\sqrt{x^{2}+1}, g(x)=\dfrac{x+1}{x^{2}+1}, h(x)=2 x-3$, then $f^{\prime}\left(h^{\prime}\left(g^{\prime}(x)\right)\right)=$

The derivative of $\sin \left(\log \left(\dfrac{x+3}{x}\right)\right)$ is

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

A particle is fired straight up from the ground. Its height in feet after $t$ second is given by $s(t)=128 t-16 t^{2}$. The velocity of the particle when it hits the ground is...

For $N \in \mathbb{N}, \dfrac{d^{\mathrm{n}}}{d x^{\mathrm{n}}}(\log x)=$

The rate of change of the volume of a sphere with respect to its surface area, when the radius is 5 m is

The approximate value of $(3.978)^{\dfrac{3}{2}}$ is

The approximate value of $x^{3}-2 x^{2}+3 x+2$ at $x=2.01$ is