What is (\partial)/(\partial x)((sin(y))/(x^2+1)) ?

The answer to (\partial)/(\partial x)((sin(y))/(x^2+1)) is -(2xsin(y))/((x^2+1)^2)

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(\partial)/(\partial x)((sin(y))/(x^2+1))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 10 x - x^{2} d x

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\frac{1}{x}, - 1

\int \frac{3 x ^{5}}{5 - 12 x ^{6}} d x

\int_{1}^{e} \frac{2}{x} d x

What is (\partial)/(\partial x)((sin(y))/(x^2+1)) ?
The answer to (\partial)/(\partial x)((sin(y))/(x^2+1)) is -(2xsin(y))/((x^2+1)^2)