What is (\partial)/(\partial x)(arcsin(x-y)) ?

The answer to (\partial)/(\partial x)(arcsin(x-y)) is 1/(sqrt(1-x^2+2xy-y^2))

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(\partial)/(\partial x)(arcsin(x-y))

\frac{\partial}{\partial x} (arcsin (x - y))

\frac{1}{1 - x ^{2} + 2 x y - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (x - y))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{1 - ( x - y ) ^{2}} \frac{\partial}{\partial x} (x - y)

= \frac{1}{1 - ( x - y ) ^{2}} \frac{\partial}{\partial x} (x - y)

\frac{\partial}{\partial x} (x - y) = 1

= \frac{1}{1 - ( x - y ) ^{2}} \cdot 1

Simplify

\frac{1}{1 - ( x - y ) ^{2}} \cdot 1 : \frac{1}{1 - x ^{2} + 2 x y - y ^{2}}

= \frac{1}{1 - x ^{2} + 2 x y - y ^{2}}

\int (x^{n}) d x

x e^{- x^{2}}

y^{^{'}} = - \frac{1}{2} y + x

\int_{0}^{2} π ((x - 1)^{2})^{2} d x

y = b^{2} (a - x) 3

What is (\partial)/(\partial x)(arcsin(x-y)) ?
The answer to (\partial)/(\partial x)(arcsin(x-y)) is 1/(sqrt(1-x^2+2xy-y^2))