Embibe Experts Solutions for Exercise 2: EXERCISE

If $y=\sin \left(4x+\frac{2\pi }{3}\right),$ then the value of $\frac{dy}{dx}$ is

If $y={\log }_e{x}^2,$ then the value of $\frac{dy}{dx}$ is

If $y=x\sin x^2,$ then the value of $\frac{dy}{dx}$ is

Let $y=50t-5t^2,$ then the value of $y$ is maximum, when $t=$

The position of a particle $x$ depends on time $t$ according to the relation $x=\left(3 \mathrm{m} {\mathrm{s}}^{–1}\right)t-\left(1 \mathrm{m} {\mathrm{s}}^{–2}\right)t^2.$ The speed of the particle at $t=2 \mathrm{s}$ is

Find the value of $\frac{d}{dx}{\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)}^2.$