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List of top Mathematics Questions on Differentiation

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:
Find the derivative of the function: \[ f(x) = 3x^3 - 5x^2 + 2x - 4 \]
Find the derivative of \( f(x) = 4x^3 - 6x^2 + 2x - 5 \).
Find the derivative of \( f(x) = 3x^2 - 4x + 7 \).
If  \(f(x) = \frac{\log(\pi + x)}{\log(e + x) }\), then the function is: