Definition of Gradient (AQA A-Level Mathematics): Flashcards

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Definition of Gradient
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dydx\frac{dy}{dx} of y=ekxy = e^{kx}

kekxke^{kx}

dydx\frac{dy}{dx} of y=6e3xy = 6e^{3x}

18e3x18e^{3x}

dydx\frac{dy}{dx} of y=3exy = 3e^{x}

3ex3e^{x}

Simplify 3eln⁡(2)3e^{\ln(2)}

66

Gradient of a curve definition

Gradient of tangent to curve at a given point

Do curves have same gradient at all points?

No, different gradients at different points

3 steps to find tangent equation

Differentiate, substitute x-value, use point-slope form

Disadvantage of graphical gradient method

Only gives estimate depending on curve quality

What does algebraic method find for gradient?

A formula for gradient of a curve

Form used to find tangent line equation

Point-slope form

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