Differentiation (Edexcel 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}

For y=6e3xy = 6e^{3x}, what is dydx\frac{dy}{dx}?

18e3x18e^{3x}

What is the gradient of y=6e3xy = 6e^{3x} when x=2x = 2?

18e618e^{6}

What does 3eln⁡(2)3e^{\ln(2)} simplify to?

66

How is the gradient of a curve at a point defined?

Gradient of tangent at that point

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

66

Do curves have the same gradient at all points?

No, different gradients at different pts

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

(ln⁡(2),6)(\ln(2), 6)

First step when finding a tangent line equation?

Differentiate the function

What is a disadvantage of estimating gradients from plots?

Only gives estimate, depends on drawing

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Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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