Last updated on Sep 20, 2026

Rules for Differentiation (VCE SSCE Mathematical Methods): Quizzes

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Rules for Differentiation

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Using the power rule, what is $f'(x)$ if $f(x) = x^5$ ?

$5x^4$

What is the derivative of a constant function $f(x) = c$ ?

$0$

If $f(x) = 5x^2$ , what is $f'(x)$ ?

$10x$

Find $\frac{dy}{dx}$ for $y = x^3 - 2x^2 + 4$ .

$3x^2 - 4x$

In Leibniz notation, how should we treat $\frac{dy}{dx}$ ?

As a single entity, not a fraction

If $f(x) = 2x^3 - 6x$ , what is $f'(2)$ ?

$18$

For $y = x^2 - 4x$ , at what $x$ -value is the gradient 0?

$x = 2$

If a tangent makes angle of $45°$ with positive $x$ -axis, what is its gradient?

$1$

If $f'(x) > 0$ for all $x$ in an interval, the function is:

Strictly increasing

Where $f'(x) = 0$ , the function often has a:

Local maximum or minimum

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