Last updated on Sep 20, 2026

Differentiation of Different Functions (VCE SSCE Mathematical Methods): Quizzes

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Differentiation of Different Functions

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What is the unique property of $f(x) = e^x$ that makes it special in calculus?

$f'(x) = e^x$ (its own derivative)

What is the approximate value of Euler's number $e$ ?

$2.71828$

What is $\frac{d}{dx}(e^{kx})$ where $k$ is a constant?

$ke^{kx}$

Find $\frac{d}{dx}(e^{-2x})$

$-2e^{-2x}$

What is $\frac{d}{dx}(e^{x^2})$ ?

$2xe^{x^2}$

What is $\frac{d}{dx}(\log_e(5x))$ for $x > 0$ ?

$\frac{1}{x}$

Find $\frac{d}{dx}(\log_e(5x + 3))$

$\frac{5}{5x + 3}$

What is $\frac{d}{dx}(\log_e(x^2 + 2))$ ?

$\frac{2x}{x^2 + 2}$

What is the gradient of $y = e^{2x} + 4$ at point $(0, 5)$ ?

$2$

What is the chain rule formula for $\frac{d}{dx}(\log_e(f(x)))$ ?

$\frac{f'(x)}{f(x)}$

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