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

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

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