List of top Mathematics Questions on Differentiation asked in Bihar Board XII

Find the derivative: \[ \frac{d}{dx} \left[ \sin^{-1}\left( 2x \sqrt{1 - x^2} \right) \right] \]
Find the derivative of \[ \frac{d}{dx} \left\{ \left| x \right|^2 \right\}. \]
Find \( \frac{d}{dx} \left(e^{3-2x}\right) \).
Find \( \frac{d}{dx} \left( \log 5x \right) \).
\(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
Find \(\frac{dy}{dx}\) when \[ (\sin y)^x = (\cos x)^y. \]
If \[ x \cos y = \sin(x + y), \] find \(\frac{dy}{dx}\).
Differentiate \[ \tan^{-1} \left( \frac{2x}{1 - x^2} \right) \] with respect to \[ \sin^{-1} \left( \frac{2x}{1 + x^2} \right). \]
If \[ y = x^{\sin x}, \] find \(\frac{dy}{dx}\).
If \[ x = \sqrt{1 + t^2}, \quad y = \sqrt{1 - t^2}, \] then find \(\frac{dy}{dx}\).
Find \( \frac{dy}{dx} \) if \[ y = \sqrt{\sin x^2}. \]
If \( y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \ldots \text{ to } \infty}}} \), then \( \frac{dy}{dx} = \):
If \( x = a \sec \theta, \, y = b \tan \theta \), then \( \frac{dy}{dx} = \):
Find the derivative of \( \sin^2 x \): \[ \frac{d}{dx} \left( \sin^2 x \right) \]
Find the derivative of \( x^5 + \cos 2x \): \[ \frac{d}{dx} \left( x^5 + \cos 2x \right) \]
Find the derivative of \( \sec^{-1}(x) \): \[ \frac{d}{dx} \left( \sec^{-1}(x) \right) \]
Find the derivative of \( a^x \): \[ \frac{d}{dx} \left( a^x \right) \]
Find the derivative of \( \log(\cos x) \): \[ \frac{d}{dx} \left( \log(\cos x) \right) \]
The slope of the tangent to the curve \( y = 2x^P + 3\sin x \) at \( x = 0 \) is:
The rate of change of the area of a circle with respect to its radius \( r \) (in cm\(^2\)/cm) at \( r = 6 \) cm is:
\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?
\(\dfrac{d}{dx}\left(11^x\right)=\) ?
\(\dfrac{d}{dx}\left(\dfrac{1}{3x-2}\right)=\) ?
If \(x=a\cos^2\theta,\ y=b\sin^2\theta\), then the value of \(\dfrac{dy}{dx}\) is
\(\dfrac{d}{dx}\big(\sin2x+e^{x}-\cos x\big)=\) ?