List of top Mathematics Questions on Differentiation asked in WBJEE

Let \( f(x) \) be continuous on \( [0, 5] \) and differentiable in \( (0, 5) \). If \( f(0) = 0 \) and \( |f'(x)| \leq \frac{1}{5} \) for all \( x \) in \( (0, 5) \), then for all \( x \) in \( [0, 5] \):
If \( f \) is the inverse function of \( g \) and \( g'(x) = \frac{1}{1+x^n} \), then the value of \( f'(x) \) is:
Let \( f \) be a function which is differentiable for all real \( x \). If \( f(2) = -4 \) and \( f'(x) \geq 6 \) for all \( x \in [2, 4] \), then:
Let $f(x) = a_0 + a_1|x| + a_2|x^2| + a_3|x^3|$, where $a_0, a_1, a_2, a_3$ are real constants. Then $f(x)$ is differentiable at $x = 0$
If $y = e^{\tan^{-1} x}$, then
Let $f(x) = \int \cos x \sin x \, e^{-t^2} dt$. Then $f' \left( \frac{\pi}{4} \right)$ equals
Let $f(x) = x^2 + x \sin x - \cos x$. Then