Quotient Rule (Leaving Cert Mathematics): Quizzes

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Quotient Rule
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What is the quotient rule used for?

Finding derivatives of quotients

For y=uvy=\frac{u}{v}, what is dydx\frac{dy}{dx}?

vdudx−udvdxv2\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}

In the quotient rule formula, what is the denominator?

v2v^2

For y=x2+1x2−1y=\frac{x^2+1}{x^2-1}, what is uu?

x2+1x^2+1

For y=exln⁡(x)y=\frac{e^x}{\ln(x)}, what is vv?

ln⁡(x)\ln(x)

For y=x2+1x2−1y=\frac{x^2+1}{x^2-1}, what is u′u'?

2x2x

For y=x2e3xy=\frac{x^2}{e^{3x}}, what is v′v'?

3e3x3e^{3x}

What is the simplified derivative of y=x2+1x2−1y=\frac{x^2+1}{x^2-1}?

−4x(x2−1)2\frac{-4x}{(x^2-1)^2}

What is the simplified derivative of y=x2e3xy=\frac{x^2}{e^{3x}}?

2x−3x2e3x\frac{2x-3x^2}{e^{3x}}

What is the first step when using the quotient rule?

Identify the numerator and denominator

In the quotient rule numerator, what order appears?

vdudx−udvdxv\frac{du}{dx}-u\frac{dv}{dx}

For y=exln⁡(x)y=\frac{e^x}{\ln(x)}, what is v′v'?

1x\frac{1}{x}

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