Chain Rule (Edexcel A-Level Mathematics): Quizzes

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Chain Rule
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What is the chain rule formula for y=f(g(x))y = f(g(x))?

dydx=f(g(x))g(x)\frac{dy}{dx} = f'(g(x)) \cdot g'(x)

Which function requires the chain rule?

ex2+2e^{x^2 + 2}

What is dydx\frac{dy}{dx} for y=sin(3x)y = \sin(3x)?

3cos(3x)3\cos(3x)

What is dydx\frac{dy}{dx} for y=ln(5x2+1)y = \ln(5x^2 + 1)?

10x5x2+1\frac{10x}{5x^2 + 1}

What is dydx\frac{dy}{dx} for y=e1xy = e^{-\frac{1}{x}}?

e1xx2\frac{e^{-\frac{1}{x}}}{x^2}

In Leibniz notation, the chain rule is written as:

dydx=dydududx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}

What is dydx\frac{dy}{dx} for y=sin(ln(3x))y = \sin(\ln(3x))?

cos(ln(3x))x\frac{\cos(\ln(3x))}{x}

What is dydx\frac{dy}{dx} for y=(x4+3)10y = (x^4 + 3)^{10}?

40x3(x4+3)940x^3(x^4 + 3)^9

For y=(x2+1)8y = (x^2 + 1)^8, the only stationary point occurs at:

x=0x = 0

What is the standard derivative ddx(ln(x))\frac{d}{dx}(\ln(x))?

1x\frac{1}{x}

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