Last updated on Sep 20, 2026

Differentiating Rational Powers (VCE SSCE Mathematical Methods): Quizzes

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Differentiating rational powers

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Which expression equals $\sqrt[3]{x}$ ?

$x^{\frac{1}{3}}$

Using the power rule, what is $\frac{d}{dx}(x^{\frac{2}{7}})$ ?

$\frac{2}{7}x^{-\frac{5}{7}}$

What is the derivative of $f(x) = x^{\frac{1}{2}}$ ?

$\frac{1}{2\sqrt{x}}$

Why do we require $x > 0$ when differentiating fractional powers?

$(-3)^{\frac{1}{2}}$ not defined in reals

The reciprocal derivative relationship states $\frac{dy}{dx} =$ ?

$\frac{1}{\frac{dx}{dy}}$

Why does $y = x^{\frac{1}{3}}$ have a vertical tangent at origin?

Derivative undefined (div by zero)

What is $\frac{d}{dx}(2x^{-\frac{1}{5}})$ ?

$-\frac{2}{5}x^{-\frac{6}{5}}$

What algebraic technique simplifies $\frac{\sqrt{x+h} - \sqrt{x}}{h}$ in first principles?

Multiply by conjugate

As denominator increases in $x^{\frac{1}{n}}$ , how does growth change?

Function grows more slowly

Using chain rule, what is $\frac{d}{dx}[(x^2 + 2x)^{\frac{1}{3}}]$ ?

$\frac{2x+2}{3(x^2+2x)^{\frac{2}{3}}}$

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Differentiating Rational Powers (VCE SSCE Mathematical Methods): Quizzes

Practise the questions

Which expression equals x3\sqrt[3]{x}3x​?

Using the power rule, what is ddx(x27)\frac{d}{dx}(x^{\frac{2}{7}})dxd​(x72​)?

What is the derivative of f(x)=x12f(x) = x^{\frac{1}{2}}f(x)=x21​?

Why do we require x>0x > 0x>0 when differentiating fractional powers?

The reciprocal derivative relationship states dydx=\frac{dy}{dx} = dxdy​= ?

Why does y=x13y = x^{\frac{1}{3}}y=x31​ have a vertical tangent at origin?

What is ddx(2x−15)\frac{d}{dx}(2x^{-\frac{1}{5}})dxd​(2x−51​)?

What algebraic technique simplifies x+h−xh\frac{\sqrt{x+h} - \sqrt{x}}{h}hx+h​−x​​ in first principles?

As denominator increases in x1nx^{\frac{1}{n}}xn1​, how does growth change?

Using chain rule, what is ddx[(x2+2x)13]\frac{d}{dx}[(x^2 + 2x)^{\frac{1}{3}}]dxd​[(x2+2x)31​]?

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Antidifferentiation of Polynomial Functions

The Second Derivative

Sketching Graphs

The Derivative

Rules for Differentiation

Differentiating Where n is a Negative Integer

The Graph of the Derivative Function

The Chain Rule

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Antidifferentiation of Polynomial Functions

The Second Derivative

Sketching Graphs

The Derivative

Rules for Differentiation

Differentiating Where n is a Negative Integer

The Graph of the Derivative Function

The Chain Rule

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Explore VCE SSCE Mathematical Methods Flashcards by Topics

Antidifferentiation of Polynomial Functions

The Second Derivative

Sketching Graphs

The Derivative

Rules for Differentiation

Differentiating Where n is a Negative Integer

The Graph of the Derivative Function

The Chain Rule

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

Which expression equals $\sqrt[3]{x}$ ?

Using the power rule, what is $\frac{d}{dx}(x^{\frac{2}{7}})$ ?

What is the derivative of $f(x) = x^{\frac{1}{2}}$ ?

Why do we require $x > 0$ when differentiating fractional powers?

The reciprocal derivative relationship states $\frac{dy}{dx} =$ ?

Why does $y = x^{\frac{1}{3}}$ have a vertical tangent at origin?

What is $\frac{d}{dx}(2x^{-\frac{1}{5}})$ ?

What algebraic technique simplifies $\frac{\sqrt{x+h} - \sqrt{x}}{h}$ in first principles?

As denominator increases in $x^{\frac{1}{n}}$ , how does growth change?

Using chain rule, what is $\frac{d}{dx}[(x^2 + 2x)^{\frac{1}{3}}]$ ?