R D Sharma Solutions for Chapter: Differentiation, Exercise 1: EXERCISE

Find $\frac{dy}{dx}$, when $y=\frac{{\left(x^2-1\right)}^3\left(2x-1\right)}{\sqrt{\left(x-3\right)\left(4x-1\right)}}$ is of the form of $\frac{{\left(x^2-1\right)}^3\left(2x-1\right)}{\sqrt{\left(x-3\right)\left(4x-1\right)}}\left\{\frac{ax}{x^2-1}+\frac{b}{2x-1}-\frac{c}{2\left(x-3\right)}-\frac{d}{4x-1}\right\}$ then $a+b+c+d=$

Find $\frac{dy}{dx}$, when $y=\frac{e^{ax}\sec x \log x}{\sqrt{1-2x}}$ is of the form of $=\frac{e^{ax} \sec x \log x}{\sqrt{1-2x}}\left(a+\tan x+\frac{1}{x \log x}+\frac{1}{1-bx}\right)$ then $b=$

Find $\frac{dy}{dx}$, when   $y={\left(\sin x\right)}^x+{\sin }^{-1}\sqrt{x}$

Find $\frac{dy}{dx}$, when   $y=x^{\cos x}+{\left(\sin x\right)}^{\tan x}$

Find $\frac{dy}{dx}$, when $y=x^x+{\left(\sin x\right)}^x$

Find $\frac{dy}{dx}$, when   $y={\left(\tan x\right)}^{\log x}+{\cos }^2\left(\frac{\pi }{4}\right)$

Find $\frac{dy}{dx}$, when    $y=x^x+x^{\frac{1}{x}}$

Find $\frac{dy}{dx}$, when  $y=x^{\log x}+{\left(\log x\right)}^x$