Practice — Calculus - Differentiation

Easy

If \( f(x) = 5x^3 - 2x + 7 \), what is \( f'(x) \)?

Easy

Find the derivative of \( y = \sin(3x) \).

Medium

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

Medium

Differentiate \( y = e^{2x} \sin x \).

Medium

Find \( \frac{dy}{dx} \) if \( y = \tan^{-1}(x^2) \).

Hard

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

Hard

Evaluate \( \frac{d}{dx} \left( \frac{\sin x}{x} \right) \) for \( x \neq 0 \).

Medium

If \( y = \ln(\sin x) \), find \( \frac{dy}{dx} \) where \( 0 < x < \pi \).

Hard

Differentiate \( y = x \cdot e^{\frac{1}{x}} \) for \( x \neq 0 \).

Hard

Find the second derivative \( \frac{d^2y}{dx^2} \) if \( y = \ln(x^2 + 1) \).

Calculus - Differentiation