What is the derivative of arcsin(x/(x+y)) ?

The derivative of arcsin(x/(x+y)) is (-x\frac{dy)/(dx)+y}{(x+y)sqrt(2xy+y^2)}

What is the first derivative of arcsin(x/(x+y)) ?

The first derivative of arcsin(x/(x+y)) is (-x\frac{dy)/(dx)+y}{(x+y)sqrt(2xy+y^2)}

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\frac{d}{d x} (arcsin (\frac{x}{x + y}))

\frac{- x \frac{d y}{d x} + y}{( x + y ) 2 x y + y ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{x + y}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{x + y}) = \frac{- x \frac{d y}{d x} + y}{( x + y ) ^{2}}

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

Simplify

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

= \frac{- x \frac{d y}{d x} + y}{( x + y ) 2 x y + y ^{2}}

y^{^{'}} = \frac{( x ^{2} + y ^{2} )}{( 2 x y )}

f (x) = ∣ 2 x - 1 ∣

y^{^{'}} + 5 y = 6 e^{x}

\frac{\partial}{\partial y} (2 y + z)

x \to 2 lim (\frac{2 x + 3}{x - 2})

What is the derivative of arcsin(x/(x+y)) ?
The derivative of arcsin(x/(x+y)) is (-x\frac{dy)/(dx)+y}{(x+y)sqrt(2xy+y^2)}
What is the first derivative of arcsin(x/(x+y)) ?
The first derivative of arcsin(x/(x+y)) is (-x\frac{dy)/(dx)+y}{(x+y)sqrt(2xy+y^2)}