What is the derivative of arcsin(y/(sqrt(x^2+y^2))) ?

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

What is the first derivative of arcsin(y/(sqrt(x^2+y^2))) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{3 x - 4}{x ^{2} - 2 x} d x

\int 3 x^{2} d x

\int 4 x^{3} - 3 x^{2} + 5 d x

\int (3 x^{2} y^{- 2} + 2 x y^{- 1}) d x

\frac{d}{d x} (\frac{( x + 1 ) ( 3 x - 7 )}{3 x + 1})

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