List of top Mathematics Questions on Differentiation asked in CBSE CLASS XII

Find the differential of \( x^{\cot x} + \frac{2x^2-3}{2x^2-x+2} \) with respect to \( x \).

If \( y\sqrt{x^2+1} = \log (\sqrt{x^2+1}-x) \), show that \( (x^2+1) \frac{dy{dx} + xy + 1 = 0 \).}

Derivative of \( \cos^{-1} \left( \frac{\sin x + \cos x}{\sqrt{2}} \right) \), \( -\frac{\pi}{4} < x < \frac{\pi}{4} \) with respect to \( x \) is :

If \( y\sqrt{x^2+1} = \log(\sqrt{x^2+1} - x) \), show that \( (x^2+1)\frac{dy{dx} + xy + 1 = 0 \).}

Find the differential of \( x^{\cot x} + \frac{2x^2-3}{2x^2-x+2} \) with respect to \( x \).

Derivative of \( \cos^{-1} \left( \frac{\sin x + \cos x}{\sqrt{2}} \right), -\frac{\pi{4} < x < \frac{\pi}{4} \) with respect to \( x \) is :}

Differentiate \(\tan^{-1}\left(\frac{\sqrt{1+x^2} - \sqrt{1-x^2}}{\sqrt{1+x^2} + \sqrt{1-x^2}}\right)\) with respect to \(\cos^{-1} x^2\).

Differential of \(e^{e^x}\) with respect to x is :

If \( x + y = xy \), then \( \frac{dy}{dx} \) is

If \( \sqrt{3}(x^2 + y^2) = 4xy \), then find \( \frac{dy}{dx} \) at \( \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) \).

If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).

Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).

If $y\sqrt{x^2 + 1} = \log\left(\sqrt{x^2 + 1} - x\right)$, show that: \[ (x^2 + 1)\frac{dy}{dx} + xy + 1 = 0 \]

Find the derivative of the composite algebraic-trigonometric function expression with respect to $x$: \[ f(x) = x^{\cot x} + \frac{2x^2 - 3}{2x^2 - x + 2} \]

Derivative of \( \cos^{-1}\left( \frac{\sin x + \cos x}{\sqrt{2}} \right) \), \( -\frac{\pi}{4} < x < \frac{\pi}{4} \) with respect to \( x \) is :

If $x=\sin t-\cos t$ and $y=\sin t\cos t$, find $\dfrac{dy}{dx}$ at $t=\dfrac{\pi}{4}$.

If $e^{x+y}+y=3x$, then $\dfrac{dy}{dx}$ is

Find the local maxima and local minima of the function \[ f(x) = \frac{8}{3} x^3 - 12x^2 + 18x + 5. \]

Differentiate \(\frac{\sin x}{\sqrt{\cos x}}\) with respect to x.

Differentiate \( y = \sqrt{\log \sin \left( \frac{x^3}{3} - 1 \right)} \) with respect to \( x \).

If \( \sqrt{1 - x^2} + \sqrt{1 - y^2} = a(x - y) \), then prove that \( \frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} \).

Differentiate: \[ \frac{\tan^{-1}\left(\frac{\sqrt{1 - x^2}}{x}\right)}{x} \quad \text{w.r.t.} \quad \cos^{-1}(2x\sqrt{1 - x^2}), \quad x \in \left(\frac{1}{\sqrt{2}}, 1\right) \]