Differentiating Powers of x (AQA A-Level Mathematics): Quizzes

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Differentiating Powers of x
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What is the derivative of xnx^n where n∈Rn \in \mathbb{R}?

nxn−1nx^{n-1}

Find dydx\frac{dy}{dx} if y=x2+3xy = x^2 + 3x.

2x+32x + 3

How must x\sqrt{x} be written before differentiating?

x12x^{\frac{1}{2}}

What is ddx(x12)\frac{d}{dx}(x^{\frac{1}{2}})?

12x−12\frac{1}{2}x^{-\frac{1}{2}}

If f(x)=10x2+x12f(x) = 10x^2 + x^{\frac{1}{2}}, what is f′(4)f'(4)?

3214\frac{321}{4}

Before differentiating, where can xx NOT appear?

On the denominator

How should 25x\frac{2}{5x} be rewritten as a power of xx?

25x−1\frac{2}{5}x^{-1}

What is dydx\frac{dy}{dx} if y=25x−1y = \frac{2}{5}x^{-1}?

−25x−2-\frac{2}{5}x^{-2}

How is x3\sqrt[3]{x} expressed as a power of xx?

x13x^{\frac{1}{3}}

Simplify x3x13\frac{x^3}{x^{\frac{1}{3}}} before differentiating.

x83x^{\frac{8}{3}}

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