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Revision:Differentiation

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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Differentiation

Differentiation allows us to find rates of change, for example, it allows us to find the rate of change of gradient on a curve. There are a number of simple rules which can be used to work out the derivative easily.

(diagram missing)

1 Notation
2 Finding the Gradient of a Curve
- 2.1 Example
3 Comments

Notation

There are a number of ways of writing the derivative:

If $\displaystyle y = x^2,\ \frac{dy}{dx} = 2x$
This means that if $\displaystyle y = x^2$ , the derivative of $\displaystyle y$ , with respect to $\displaystyle x$ is $\displaystyle 2x$ .
$\displaystyle \frac{d (x^2)}{dx} = 2x$
This says that the derivative of $\displaystyle x^2$ with respect to $\displaystyle x$ is $\displaystyle 2x$ .
If $\displaystyle f(x) = x^2,\ f'(x) = 2x$
This says that is $\displaystyle f(x) = x^2$ , the derivative of $\displaystyle f(x)$ is $\displaystyle 2x$ .

Finding the Gradient of a Curve

Example

What is the gradient of the curve $\displaystyle y = 2x^3$ when

$\displaystyle x = 3$ .

$\displaystyle \frac{dy}{dx} = 6x^2$

When $\displaystyle x = 3,\ \frac{dy}{dx} = 6\times 9 = 54$ .

Comments

This is a rather basic article - perhaps not enough detail to explain what differentiation is and how to do it. Needs the general rule including for basic polynomials (with positive whole number powers for C1 and fractional and negative powers for C2).

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