Science (English Medium) Class 12 - CBSE Question Bank Solutions

If \[\sin y = x \sin \left( a + y \right), \text { then }\frac{dy}{dx} \text { is}\] ____________ .

The derivative of \[\cos^{- 1} \left( 2 x^2 - 1 \right)\] with respect to  \[\cos^{- 1} x\]  is ___________ .

If \[f\left( x \right) = \sqrt{x^2 + 6x + 9}, \text { then } f'\left( x \right)\] is equal to ______________ .

If \[f\left( x \right) = \left| x^2 - 9x + 20 \right|\]  then `f' (x)` is equal to ____________ .

If \[f\left( x \right) = \sqrt{x^2 - 10x + 25}\]  then the derivative of f (x) in the interval [0, 7] is ____________ .

If \[f\left( x \right) = \left| x - 3 \right| \text { and }g\left( x \right) = fof \left( x \right)\]  is equal to __________ .

If \[f\left( x \right) = \left( \frac{x^l}{x^m} \right)^{l + m} \left( \frac{x^m}{x^n} \right)^{m + n} \left( \frac{x^n}{x^l} \right)^{n + 1}\] the f' (x) is equal to _____________ .

If \[y = \frac{1}{1 + x^{a - b} +^{c - b}} + \frac{1}{1 + x^{b - c} + x^{a - c}} + \frac{1}{1 + x^{b - a} + x^{c - a}}\] then \[\frac{dy}{dx}\]  is equal to ______________ .

If  \[\sqrt{1 - x^6} + \sqrt{1 - y^6} = a^3 \left( x^3 - y^3 \right)\] then \[\frac{dy}{dx}\] is equal to ____________ .

If \[y = \log \sqrt{\tan x}\] then the value of \[\frac{dy}{dx}\text { at }x = \frac{\pi}{4}\] is given by __________ .

If \[\sin^{- 1} \left( \frac{x^2 - y^2}{x^2 + y^2} \right) = \text { log a then } \frac{dy}{dx}\] is equal to _____________ .

If \[\sin y = x \cos \left( a + y \right), \text { then } \frac{dy}{dx}\] is equal to ______________ .

If \[y = \log \left( \frac{1 - x^2}{1 + x^2} \right), \text { then } \frac{dy}{dx} =\] __________ .

If \[y = \sqrt{\sin x + y}, \text { then }\frac{dy}{dx} \text { equals }\] ______________ .

If \[y = \tan^{- 1} \left( \frac{\sin x + \cos x}{\cos x - \sin x} \right), \text { then  } \frac{dy}{dx}\] is equal to ___________ .

Find the second order derivatives of the following function  x³ + tan x ?

Find the second order derivatives of the following function sin (log x) ?

Find the second order derivatives of the following function  log (sin x) ?

Find the second order derivatives of the following function e^x sin 5x  ?

Find the second order derivatives of the following function e^6x cos 3x  ?