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

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

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

Differentiate \[e^{\sin^{- 1} 2x}\] ?

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

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

Differentiate \[\sqrt{\tan^{- 1} \left( \frac{x}{2} \right)}\] ?

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

Differentiate \[\frac{2^x \cos x}{\left( x^2 + 3 \right)^2}\]?

Differentiate \[x \sin 2x + 5^x + k^k + \left( \tan^2 x \right)^3\] ?

Differentiate \[\log \left( 3x + 2 \right) - x^2 \log \left( 2x - 1 \right)\] ?

Differentiate \[\frac{3 x^2 \sin x}{\sqrt{7 - x^2}}\] ?

Differentiate \[\sin^2 \left\{ \log \left( 2x + 3 \right) \right\}\] ?

Differentiate  \[e^x \log \sin 2x\] ?

Differentiate \[\frac{\sqrt{x^2 + 1} + \sqrt{x^2 - 1}}{\sqrt{x^2 + 1} - \sqrt{x^2 - 1}}\] ?

Differentiate \[\left( \sin^{- 1} x^4 \right)^4\] ?

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

Differentiate \[\frac{e^x \sin x}{\left( x^2 + 2 \right)^3}\] ?

Differentiate \[3 e^{- 3x} \log \left( 1 + x \right)\] ?

Differentiate \[\frac{x^2 + 2}{\sqrt{\cos x}}\] ?

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