List of top Mathematics Questions on Differentiation asked in VITEEE

Find the derivative of the function: \[ f(x) = 3x^3 - 5x^2 + 2x - 4 \]

If \( |x + 3| + x>1 \), then \( x \in \):

If \( y = \tan^{-1} \left( \frac{4x}{1+5x^2} \right) + \tan^{-1} \left( \frac{2 + 3x}{3 - 2x} \right) \), then \( \frac{dy}{dx} = \):

If \( \sin y = x \sin(a + y) \), then \( \frac{dy}{dx} \) is equal to:

A value of \( c \) for which conclusion of Mean Value Theorem holds for the function \( f(x) = \log x \) on the interval [1, 3] is

If \( y = 2^x \), then \[ \frac{dy}{dx} \, \text{at} \, x = e \, \text{is} \]

If the tangent to the function \( y = f(x) \) at \( (3, 4) \) makes an angle of \( \frac{3\pi}{4} \) with the positive direction of the x-axis in anticlockwise direction, then \( f'(3) \) is

If \( R \to R \) be such that \( f(1) = 3 \) and \( f'(1) = 6 \), then \( f(x) \) is equal to

If \(x=\sec\theta-\cos\theta,\ y=\sec^n\theta-\cos^n\theta\), then \((x^2+4)\left(\dfrac{dy}{dx}\right)\) is equal to

If \(y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\cdots}}}}\), then \(\dfrac{dy}{dx}\) is equal to

If
\[ x=\cos^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), \quad y=\sin^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right), \] then \(\frac{dy}{dx}\) is equal to

If
\[ \frac{d}{dx}\left[a\tan^{-1}x+b\log\left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1} \] then \(a-2b\) is equal to

If
\[ y=e^{a\sin^{-1}x}=(1-x^2)y_{n+2}-(2n+1)xy_{n+1} \] is equal to

If \( (x + y) \sin u = x^2 y^2 \), then \( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \) is

If the normal to the curve \( y = f(x) \) at \( (3, 4) \) makes an angle \( \frac{3\pi}{4} \) with the positive x-axis, then \( f'(3) \) is equal to

If \( f(2) = 4 \) and \( f'(2) = 1 \), then \[ \lim_{x \to 2} \frac{x f(2) - 2f(x)}{x - 2} \text{ is equal to:} \]

If \( u = \tan^{-1} \left( \frac{x^3 + y^2}{x + y} \right) \), then \( \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} \) is: