A-level Mathematics/Edexcel/Core 1/Differentiation

Differentiation is the opposite to integration and you use dy/dx. To differentiate an equation, you drop the power in the front of the equation and you decrease the power by 1.

E.g. $y=3x^2+4x^5$ becomes

$\frac{dy}{dx}=6x^1+20x^4$ or $\frac{dy}{dx}=6x+20x^4$

By substituting x values into dy/dx, you are able to find the gradient at a certain point on a graph.

$\frac{dy}{dx}$ is known as the first deriative of an equation. $\frac{dy}{dx}$ is known as the second deriative. It is first deriative differentiated a second time.

Continuing from the example above,

$\frac{dy}{dx}=6x+20x^4$ becomes

$\frac{d^{2}y}{d{x}^2}=6+80x^3$

The deriatives can be displayed in a few different ways in questions. It can be presented as dy/dx or f'(x).