Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

If \[y = \left\{ \log_{\cos x} \sin x \right\} \left\{ \log_{\sin x} \cos x \right\}^{- 1} + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right), \text{ find } \frac{dy}{dx} \text{ at }x = \frac{\pi}{4}\] ?

If \[\sqrt{y + x} + \sqrt{y - x} = c, \text {show that } \frac{dy}{dx} = \frac{y}{x} - \sqrt{\frac{y^2}{x^2} - 1}\] ?

Differentiate \[x^{1/x}\]  with respect to x.

Differentiate \[x^{\sin x}\]  ?

Differentiate \[\left( 1 + \cos x \right)^x\] ?

Differentiate \[x^{\cos^{- 1} x}\] ?

Differentiate \[\left( \log x \right)^x\] ?

Differentiate \[\left( \log x \right)^{\cos x}\] ?

Differentiate \[\left( \sin x \right)^{\cos x}\] ?

Differentiate \[e^{x \log x}\] ?

Differentiate  \[\left( \sin x \right)^{\log x}\] ?

Differentiate \[{10}^{ \log \sin x }\] ?

Differentiate \[\left( \log x \right)^{ \log x }\] ?

Differentiate \[{10}^\left( {10}^x \right)\] ?

Differentiate  \[\sin \left( x^x \right)\] ?

Differentiate \[\left( \sin^{- 1} x \right)^x\] ?

Differentiate \[x^{\sin^{- 1} x}\]  ?

Differentiate \[\left( \tan x \right)^{1/x}\] ?

Differentiate \[x^{\tan^{- 1} x }\]  ?

Differentiate  \[\left( x^x \right) \sqrt{x}\] ?