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

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

Find  \[\frac{dy}{dx}\] \[y = e^x + {10}^x + x^x\] ?

find  \[\frac{dy}{dx}\]  \[y = \frac{\left( x^2 - 1 \right)^3 \left( 2x - 1 \right)}{\sqrt{\left( x - 3 \right) \left( 4x - 1 \right)}}\] ?

Find  \[\frac{dy}{dx}\]  \[y = \frac{e^{ax} \cdot \sec x \cdot \log x}{\sqrt{1 - 2x}}\] ?

Find  \[\frac{dy}{dx}\] \[y = e^{3x} \sin 4x \cdot 2^x\] ?

Find  \[\frac{dy}{dx}\] \[y = \sin x \sin 2x \sin 3x \sin 4x\] ?

Find  \[\frac{dy}{dx}\] \[y = x^{\sin x} + \left( \sin x \right)^x\] ?

Find  \[\frac{dy}{dx}\]  \[y = \left( \sin x \right)^{\cos x} + \left( \cos x \right)^{\sin x}\] ?

Find \[\frac{dy}{dx}\] \[y =  \left( \tan  x \right)^{\cot   x}  +  \left( \cot  x \right)^{\tan  x}\] ?

If `y=(sinx)^x + sin^-1 sqrtx  "then find"  dy/dx` 

Find \[\frac{dy}{dx}\] \[y = x^{\cos x} + \left( \sin x \right)^{\tan x}\] ?

Find \[\frac{dy}{dx}\]  \[y = x^x + \left( \sin x \right)^x\] ?

Find \[\frac{dy}{dx}\] \[y = \left( \tan x \right)^{\log x} + \cos^2 \left( \frac{\pi}{4} \right)\] ?

Find \[\frac{dy}{dx}\]

\[y = x^x + x^{1/x}\] ?

Find \[\frac{dy}{dx}\] \[y = x^{\log x }+ \left( \log x \right)^x\] ?

If \[x^{13} y^7 = \left( x + y \right)^{20}\] prove that \[\frac{dy}{dx} = \frac{y}{x}\] ?

If \[x^{16} y^9 = \left( x^2 + y \right)^{17}\] ,prove that \[x\frac{dy}{dx} = 2 y\] ?

If \[y = \sin \left( x^x \right)\] prove that  \[\frac{dy}{dx} = \cos \left( x^x \right) \cdot x^x \left( 1 + \log x \right)\] ?

If \[x^x + y^x = 1\], prove that \[\frac{dy}{dx} = - \left\{ \frac{x^x \left( 1 + \log x \right) + y^x \cdot \log y}{x \cdot y^\left( x - 1 \right)} \right\}\] ?