Is \frac{d}{dx}\left[(2x+5)(x-1)\right]=2\times1?

No. Expand first; the derivative is 4x+3.

How do you find where a curve has gradient k?

Differentiate, then solve \frac{dy}{dx}=k.

Differentiating powers of xEdexcel International A Level Maths: Flashcards

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Differentiate $x^n$.

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Differentiate $x^n$ .: $nx^{n-1}$
What does a constant differentiate to?: $0$
Differentiate $ax^n$ where $a$ is a constant.: $anx^{n-1}$
Differentiate $x$ .: $1$
Write $\sqrt{x}$ as a power.: $x^{\frac12}$
Write $\frac{1}{x^3}$ as a power.: $x^{-3}$
Differentiate $x^{\frac32}$ .: $\frac32x^{\frac12}$
Differentiate $\frac{4}{x}$ .: $-4x^{-2}$ , or $-\frac{4}{x^2}$
Differentiate $5\sqrt{x}$ .: $\frac52x^{-\frac12}$
First step before differentiating $(2x+5)(x-1)$ ?: Expand it to $2x^2+3x-5$ .
Rewrite $\frac{x^2+5x-3}{3x}$ in index form.: $\frac13x+\frac53-x^{-1}$
Is $\frac{\mathrm{d}}{\mathrm{d}x}\left[(2x+5)(x-1)\right]=2\times1$ ?: No. Expand first; the derivative is $4x+3$ .
How do you find where a curve has gradient $k$ ?: Differentiate, then solve $\frac{\mathrm{d}y}{\mathrm{d}x}=k$ .

Exam questions on Differentiating powers of x

A curve has equation $y=3x^4-2x^2+7x-5$ .
Find the gradient of the curve at the point where it crosses the $y$ -axis.2 marks
A curve has equation $y=f(x)$ , where $f(x)=(2x+5)(x-1)$ .
The curve crosses the positive $x$ -axis at the point $A$ . Find the gradient of the curve at $A$ .2 marks
A curve has equation $y=\dfrac{x^2+5x-3}{3x}$ for $x\neq0$ .
Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).