What is (\partial)/(\partial x)(((9y+7z))/(x+u)) ?

The answer to (\partial)/(\partial x)(((9y+7z))/(x+u)) is -(9y+7z)/((x+u)^2)

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(\partial)/(\partial x)(((9y+7z))/(x+u))

\frac{\partial}{\partial x} (\frac{( 9 y + 7 z )}{x + u})

- \frac{9 y + 7 z}{( x + u ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{( 9 y + 7 z )}{x + u})

Treat

y, z, u

as constants

Take the constant out:

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

= (9 y + 7 z) \frac{\partial}{\partial x} (\frac{1}{x + u})

Apply exponent rule:

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

= (9 y + 7 z) \frac{\partial}{\partial x} ((x + u)^{- 1})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + u) = 1

= (9 y + 7 z) (- \frac{1}{( x + u ) ^{2}} \cdot 1)

Simplify

(9 y + 7 z) (- \frac{1}{( x + u ) ^{2}} \cdot 1) : - \frac{9 y + 7 z}{( x + u ) ^{2}}

= - \frac{9 y + 7 z}{( x + u ) ^{2}}

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\int_{0}^{2} \frac{5 t}{( t - 3 ) ^{2}} d t

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What is (\partial)/(\partial x)(((9y+7z))/(x+u)) ?
The answer to (\partial)/(\partial x)(((9y+7z))/(x+u)) is -(9y+7z)/((x+u)^2)