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Temka [501]
2 years ago
13

Find dy/dx of y = sin inverse ( x - 1 ).

Mathematics
1 answer:
jolli1 [7]2 years ago
8 0

\frac{1}{ \sqrt{1 -  {(x - 1)}^{2} } }

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Vertical angles are congruent, so their measures are equal.
Set the angle measures equal and solve for x.

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6 0
3 years ago
(b) dy/dx = (x - y+ 1)^2
Elanso [62]

Substitute v(x)=x-y(x)+1, so that

\dfrac{\mathrm dv}{\mathrm dx}=1-\dfrac{\mathrm dy}{\mathrm dx}

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1-\dfrac{\mathrm dv}{\mathrm dx}=v^2\implies\dfrac{\mathrm dv}{1-v^2}=\mathrm dx

On the left, we can split into partial fractions:

\dfrac12\left(\dfrac1{1-v}+\dfrac1{1+v}\right)\mathrm dv=\mathrm dx

Integrating both sides gives

\dfrac{\ln|1-v|+\ln|1+v|}2=x+C

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3 0
3 years ago
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Answer:

Step-by-step explanation:

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