Practice — Differential Calculus

Easy

If \( f(x) = 3x^2 + 5x - 2 \), what is \( f'(x) \)?

Easy

Find the derivative of \( y = \sin(2x) \).

Easy

If \( y = \ln(x^2 + 1) \), then \( \frac{dy}{dx} = ? \)

Easy

The derivative of \( f(x) = e^{3x} \) is:

Hard

Find \( \frac{dy}{dx} \) if \( y = x^x \), \( x > 0 \).

Medium

If \( f(x) = \frac{2x+3}{x-1} \), find \( f'(x) \).

Medium

For \( y = \tan^{-1}(x^2) \), find \( \frac{dy}{dx} \).

Medium

If \( y = \sqrt{\sin x} \), find \( \frac{dy}{dx} \).

Medium

Find the equation of the tangent line to \( y = x^3 - 3x + 2 \) at \( x = 2 \).

Hard

Evaluate \( \lim_{h \to 0} \frac{\sqrt{1+h} - 1}{h} \) using derivative definition.

Differential Calculus