Inverse Trig Functions (Leaving Cert Mathematics): Quizzes

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Inverse Trig Functions
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What are derivatives of inverse trig functions particularly useful for?

Integration & implicit differentiation

What is ddxsin⁡−1(xa)\frac{d}{dx} \sin^{-1} \left(\frac{x}{a}\right)?

1a2−x2\frac{1}{\sqrt{a^2 - x^2}}

What is ddxcos⁡−1(xa)\frac{d}{dx} \cos^{-1} \left(\frac{x}{a}\right)?

−1a2−x2\frac{-1}{\sqrt{a^2 - x^2}}

What is ddxtan⁡−1(xa)\frac{d}{dx} \tan^{-1} \left(\frac{x}{a}\right)?

aa2+x2\frac{a}{a^2 + x^2}

Which inverse trig derivative gives a negative result?

cos⁡−1(x/a)\cos^{-1}(x/a)

When is the chain rule required with inverse trig functions?

For complex expressions

In the example y=sin⁡−1(1/x2)y=\sin^{-1}(1/x^2), what is the inner function vv?

1x2\frac{1}{x^2}

For u=sin⁡−1(v)u=\sin^{-1}(v) with v=1/x2v=1/x^2, what is u′u' in terms of vv?

11−v2\frac{1}{\sqrt{1-v^2}}

For v=1x2v=\frac{1}{x^2}, what is v′v'?

−2x3-\frac{2}{x^3}

What is the final answer for dydx\frac{dy}{dx} of y=sin⁡−1(1/x2)y=\sin^{-1}(1/x^2)?

−2xx4−1-\frac{2}{x\sqrt{x^4-1}}

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