New 2026 Level 3 Differentiation prediction exam is out: a full paper with worked answers, free. Try it

L3 Differentiation

Question Bank

Basic Derivatives Gradients & Rates of Change Limits & Continuity Tangents & Normals Stationary & Inflection Points Implicit Differentiation Parametric Related Rates Optimisation Kinematics Verifying Differential Equations
Achieved

Differentiate $y = \dfrac{5}{x^2} + 8\sqrt{x} - \cos 4x$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = (4 - 3x^2)^7$.

You do not need to simplify your answer.

Achieved

Differentiate $f(x) = \sqrt{2x^3 + 5}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = 4e^{1 - x^3}$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = \ln(2x^4 - x + 3)$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \dfrac{4}{\sqrt[3]{1 - 6x}}$.

You do not need to simplify your answer.

Achieved

Find $f'(x)$ when $f(x) = 3\sec(2x^2)$.

You do not need to simplify your answer.

Achieved

Differentiate $y = 2\cot\left(\dfrac{x}{4}\right)$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \sqrt[4]{(3x - 1)^3}$, $x > \dfrac{1}{3}$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = \ln\left(\dfrac{(2x + 5)^4}{x^2 + 3}\right)$, $x > -\dfrac{5}{2}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = x^3e^{-2x}$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = (2x + 1)^4(x - 3)^3$.

You do not need to simplify your answer.

Achieved

Find $f'(x)$ when $f(x) = (3 - x^2)\ln(4x + 1)$, $x > -\dfrac{1}{4}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \dfrac{\sin 4x}{x^2 + 3}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = x^2\sqrt{5 - 2x}$, $x < \dfrac{5}{2}$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = e^{3x}\sec 2x$.

You do not need to simplify your answer.

Achieved

Differentiate $y = x^2\operatorname{cosec} 3x$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \dfrac{x}{\sqrt{x^2 + 4}}$.

You do not need to simplify your answer.

Achieved

Find $f'(x)$ when $f(x) = \dfrac{e^{x^2}}{x + 3}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \sqrt{x}\cot 4x$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \dfrac{x^2 + 1}{\ln 2x}$, $x > \dfrac{1}{2}$.

You do not need to simplify your answer.

Achieved

Differentiate $g(t) = e^{4t}\ln(1 - 2t)$ with respect to $t$, for $t < \dfrac{1}{2}$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = \ln(\cos 3x)$, $0 < x < \dfrac{\pi}{6}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = [\ln(x^2 + 1)]^3$.

You do not need to simplify your answer.

Achieved

Find $f'(x)$ when $f(x) = e^{\sin^2 x}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \sin^3(2x)\cos x$.

You do not need to simplify your answer.

Achieved

Find $\dfrac{dy}{dx}$ if $y = \dfrac{\sec 3x}{1 + \tan 3x}$.

You do not need to simplify your answer.

Achieved

Differentiate $y = \sqrt{\dfrac{1 + 2x}{1 - 2x}}$, $-\dfrac{1}{2} < x < \dfrac{1}{2}$.

You do not need to simplify your answer.