Product Rule (AQA A-Level Mathematics): Quizzes

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Product Rule
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What is the product rule formula for ddx[u(x)⋅v(x)]\frac{d}{dx}[u(x) \cdot v(x)]?

u(x)⋅v′(x)+v(x)⋅u′(x)u(x) \cdot v'(x) + v(x) \cdot u'(x)

The product rule accounts for the product changing in how many ways?

Two ways

What is dydx\frac{dy}{dx} for y=x2⋅sin⁡(x)y = x^2 \cdot \sin(x)?

x2cos⁡(x)+2xsin⁡(x)x^2 \cos(x) + 2x \sin(x)

What is dydx\frac{dy}{dx} for y=ex⋅ln⁡(x)y = e^x \cdot \ln(x)?

exx+exln⁡(x)\frac{e^x}{x} + e^x \ln(x)

For y=(3x2+2x)⋅cos⁡(x)y = (3x^2 + 2x) \cdot \cos(x), what is dydx\frac{dy}{dx}?

−(3x2+2x)sin⁡(x)+(6x+2)cos⁡(x)-(3x^2 + 2x)\sin(x) + (6x + 2)\cos(x)

For y=x2⋅e3xy = x^2 \cdot e^{3x}, what is v′(x)v'(x) if v(x)=e3xv(x) = e^{3x}?

3e3x3e^{3x}

What is dydx\frac{dy}{dx} for y=xsin⁡xy = x \sin x?

sin⁡x+xcos⁡x\sin x + x \cos x

For y=x2⋅e3xy = x^2 \cdot e^{3x}, what is the factorised form of dydx\frac{dy}{dx}?

e3x(3x2+2x)e^{3x}(3x^2 + 2x)

For y=3x4e2x+3y = 3x^4 e^{2x+3}, what is the factorised form of dydx\frac{dy}{dx}?

6x3e2x+3(2+x)6x^3e^{2x+3}(2+x)

When using product rule, which functions need to be differentiated?

Both u(x)u(x) and v(x)v(x) separately

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Differentiation

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Differentiation

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Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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