What is (\partial)/(\partial x)(1-x/y) ?

The answer to (\partial)/(\partial x)(1-x/y) is -1/y

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(\partial)/(\partial x)(1-x/y)

\frac{\partial}{\partial x} (1 - \frac{x}{y})

- \frac{1}{y}

Solution steps

\frac{\partial}{\partial x} (1 - \frac{x}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (1) = 0

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

= 0 - \frac{1}{y}

Simplify

= - \frac{1}{y}

\int_{1}^{2} x e^{2 x^{2} - 3} d x

\int_{0}^{π} 10 t sin (3 t) d t

f (x) = x^{4} + 9 x^{2} - x, (1, 9)

x \to \infty lim (\frac{x \cdot ( x + 1 ) ^{x + 1}}{( x + 1 ) ^{x + 2}})

\frac{1}{( 8 ^{2} + 1 ) + ( 8 ^{2} + 4 )}

What is (\partial)/(\partial x)(1-x/y) ?
The answer to (\partial)/(\partial x)(1-x/y) is -1/y