PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions

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  \[\left( x^x \right) \sqrt{x}\] ?

Differentiate \[x^\left( \sin x - \cos x \right) + \frac{x^2 - 1}{x^2 + 1}\] ?