What is (\partial)/(\partial x)(-1/(10+2xy)) ?

The answer to (\partial)/(\partial x)(-1/(10+2xy)) is y/(2(xy+5)^2)

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(\partial)/(\partial x)(-1/(10+2xy))

\frac{\partial}{\partial x} (- \frac{1}{10 + 2 x y})

\frac{y}{2 ( x y + 5 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (- \frac{1}{10 + 2 x y})

Treat

y

as a constant

Take the constant out:

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

= - \frac{\partial}{\partial x} (\frac{1}{10 + 2 x y})

Apply exponent rule:

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

= - \frac{\partial}{\partial x} ((10 + 2 x y)^{- 1})

Apply the chain rule:

- \frac{1}{( 10 + 2 x y ) ^{2}} \frac{\partial}{\partial x} (10 + 2 x y)

= - \frac{1}{( 10 + 2 x y ) ^{2}} \frac{\partial}{\partial x} (10 + 2 x y)

\frac{\partial}{\partial x} (10 + 2 x y) = 2 y

= - (- \frac{1}{( 10 + 2 x y ) ^{2}} \cdot 2 y)

Simplify

- (- \frac{1}{( 10 + 2 x y ) ^{2}} \cdot 2 y) : \frac{y}{2 ( x y + 5 ) ^{2}}

= \frac{y}{2 ( x y + 5 ) ^{2}}

\int sin (\frac{nπ}{2} x) d x

ln (2 x^{2} + 1)

\frac{d}{d x} (\frac{3}{x - 8})

\int \frac{1}{sin ^{2} ( 5 x )} d x

\frac{d}{d z} (x y z)

What is (\partial)/(\partial x)(-1/(10+2xy)) ?
The answer to (\partial)/(\partial x)(-1/(10+2xy)) is y/(2(xy+5)^2)