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

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

kekxke^{kx}

What is dydx\frac{dy}{dx} for y=6e3xy = 6e^{3x}?

18e3x18e^{3x}

For y=6e3xy = 6e^{3x}, what is the gradient when x=2x = 2?

18e618e^{6}

What is dydx\frac{dy}{dx} for y=3exy = 3e^{x}?

3ex3e^{x}

What is the value of 3eln⁡(2)3e^{\ln(2)}?

66

For y=3exy = 3e^{x} at x=ln⁡(2)x = \ln(2), what is the point of tangency?

(ln⁡(2),6)(\ln(2), 6)

For y=3exy = 3e^{x} at x=ln⁡(2)x = \ln(2), what is the gradient?

66

How is the gradient of a curve defined?

Gradient of tangent at a given point

What is a disadvantage of estimating gradients graphically?

Only gives an estimate

What are the steps to find the equation of a tangent?

Differentiate, substitute x, use point-slope

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Differentiation

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Differentiation

Applications of Differentiation

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Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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