First Principles Differentiation (Edexcel A-Level Mathematics): Quizzes

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First Principles Differentiation
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What is the gradient of y=x2y = x^2?

2x2x

What is the gradient function for F(x)=xnF(x) = x^n where nRn \in \mathbb{R}?

nxn1nx^{n-1}

What is the first principles formula for the gradient of F(x)F(x)?

limh0F(x+h)F(x)h\lim_{{h \to 0}} \frac{F(x+h) - F(x)}{h}

In first principles, the chord becomes a tangent as what happens to hh?

h0h \to 0

What does the notation dydx\frac{dy}{dx} represent?

Limit as h0h \to 0 of gradient of chord

Which is NOT a name for the gradient formula?

The integral

Using the power rule, what is the gradient of y=x4y = x^4?

4x34x^3

What is the result of differentiating x2+2xx^2 + 2x by first principles?

2x+22x + 2

If y=3x2+2xy = 3x^2 + 2x, what is dydx\frac{dy}{dx} when x=1x = 1?

88

What is the first step in first principles differentiation?

Draw a chord between two points

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