Inverse Trigonometric Functions (AQA A-Level Further Maths): Quizzes

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Inverse Trigonometric Functions
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What is d(arcsin⁡x)dx\frac{d(\arcsin x)}{dx}?

11−x2\frac{1}{\sqrt{1-x^2}}

What is d(arctan⁡x)dx\frac{d(\arctan x)}{dx}?

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

How do derivatives of arcsin⁡x\arcsin x and arccos⁡x\arccos x differ?

Only by a negative sign

What is the reciprocal rule for derivatives?

dydx=1dxdy\frac{dy}{dx} = \frac{1}{\frac{dx}{dy}}

What is ∫11+x2 dx\int \frac{1}{1+x^2} \, dx?

arctan⁡x+c\arctan x + c

For integrals involving a2−x2\sqrt{a^2 - x^2}, which substitution should be used?

x=asin⁡ux = a\sin u

For integrals involving a2+x2a^2 + x^2, which substitution should be used?

x=atan⁡ux = a\tan u

What is d(arctan⁡3x)dx\frac{d(\arctan 3x)}{dx}?

31+9x2\frac{3}{1+9x^2}

Which identity is used when deriving the derivative of arcsin⁡x\arcsin x?

cos⁡2y+sin⁡2y=1\cos^2 y + \sin^2 y = 1

When should you complete the square in integration problems?

When denominator is quadratic, not standard

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