What is (\partial)/(\partial x)(5x-y+7xy) ?

The answer to (\partial)/(\partial x)(5x-y+7xy) is 7y+5

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(\partial)/(\partial x)(5x-y+7xy)

\frac{\partial}{\partial x} (5 x - y + 7 x y)

7 y + 5

Solution steps

\frac{\partial}{\partial x} (5 x - y + 7 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x) - \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (7 x y)

\frac{\partial}{\partial x} (5 x) = 5

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

\frac{\partial}{\partial x} (7 x y) = 7 y

= 5 - 0 + 7 y

Simplify

= 7 y + 5

y = - 1 + \frac{x ^{2}}{4}, y = 2 + \frac{x}{4}, [0, 4]

\frac{d}{d x} (e^{- 0.5 x^{2}})

\int_{1}^{3} (\frac{1}{x}) d x

\int (2 x^{2} + x) e^{3 x} d x

x \to 0 lim (\frac{x ^{2} - 3 x}{x})

What is (\partial)/(\partial x)(5x-y+7xy) ?
The answer to (\partial)/(\partial x)(5x-y+7xy) is 7y+5