What is (\partial)/(\partial x)(5/(5x+3y)) ?

The answer to (\partial)/(\partial x)(5/(5x+3y)) is -(25)/((5x+3y)^2)

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(\partial)/(\partial x)(5/(5x+3y))

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

- \frac{25}{( 5 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5}{5 x + 3 y})

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (\frac{1}{5 x + 3 y})

Apply exponent rule:

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

= 5 \frac{\partial}{\partial x} ((5 x + 3 y)^{- 1})

Apply the chain rule:

- \frac{1}{( 5 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (5 x + 3 y)

= - \frac{1}{( 5 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (5 x + 3 y)

\frac{\partial}{\partial x} (5 x + 3 y) = 5

= 5 (- \frac{1}{( 5 x + 3 y ) ^{2}} \cdot 5)

Simplify

5 (- \frac{1}{( 5 x + 3 y ) ^{2}} \cdot 5) : - \frac{25}{( 5 x + 3 y ) ^{2}}

= - \frac{25}{( 5 x + 3 y ) ^{2}}

\frac{10}{s ( s + 2 ) ( s + 3 ) ^{2}}

x \to 0 - lim (x sin (\frac{1}{x}))

x y^{^{'}} + y = - 5 x y^{2}, y (1) = 7

\int arccot (2 y) d y

y^{^{'}} = \frac{x y ^{3}}{16}

What is (\partial)/(\partial x)(5/(5x+3y)) ?
The answer to (\partial)/(\partial x)(5/(5x+3y)) is -(25)/((5x+3y)^2)