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

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

\[\log\left\{ \cot\left( \frac{\pi}{4} + \frac{x}{2} \right) \right\}\] ?

Differentiate \[e^{ax} \sec x \tan 2x\] ?

Differentiate \[\log \left( \cos x^2 \right)\] ?

Differentiate \[\cos \left( \log x \right)^2\] ?

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

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

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