Differentiation (Edexcel A-Level Mathematics): Flashcards

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First Principles Differentiation
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How do you find the gradient of y=x2y = x^2?

Differentiate to get dydx=2x\frac{dy}{dx} = 2x.

What happens to the chord as hh approaches 00?

The chord becomes a tangent to the curve.

What is the gradient formula for y=xny = x^n?

The gradient is given by nxn1nx^{n-1}.

What is the gradient of F(x)=x4F(x) = x^4?

The gradient is 4x34x^3.

What does the limit definition represent?

It represents the gradient of the function at a point.

How do you differentiate x2+2xx^2 + 2x using first principles?

Find the limit of (f(x+h)f(x))/h(f(x+h) - f(x)) / h as hh approaches 00.

What is another name for the gradient function?

It is also called the derivative.

What does dydx\frac{dy}{dx} signify?

It represents the rate of change of yy with respect to xx.

What does F(x)=x3F(x) = x^3 have as its gradient?

The gradient is 3x23x^2.

What is dy/dxdy/dx for y=3x2+2xy = 3x^2 + 2x?

dy/dx=6x+2dy/dx = 6x + 2

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