What is (\partial)/(\partial x)(36(x/(x+y))-x) ?

The answer to (\partial)/(\partial x)(36(x/(x+y))-x) is (36y)/((x+y)^2)-1

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(\partial)/(\partial x)(36(x/(x+y))-x)

\frac{\partial}{\partial x} (36 (\frac{x}{x + y}) - x)

\frac{36 y}{( x + y ) ^{2}} - 1

Solution steps

\frac{\partial}{\partial x} (36 (\frac{x}{x + y}) - x)

Simplify

36 (\frac{x}{x + y}) - x : \frac{36 x}{x + y} - x

= \frac{\partial}{\partial x} (\frac{36 x}{x + y} - x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (\frac{36 x}{x + y}) - \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (\frac{36 x}{x + y}) = \frac{36 y}{( x + y ) ^{2}}

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

= \frac{36 y}{( x + y ) ^{2}} - 1

(x^{2} + 1) (\frac{d y}{d x}) + 8 x (y - 1) = 0, y (0) = 6

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

x \to 5 lim (x + 2)

x \to 2 lim ((x - 1)^{2} - 1)

\frac{x + 2}{10 - 3 x}

What is (\partial)/(\partial x)(36(x/(x+y))-x) ?
The answer to (\partial)/(\partial x)(36(x/(x+y))-x) is (36y)/((x+y)^2)-1