What is (\partial)/(\partial x)(2x-8y+8xy) ?

The answer to (\partial)/(\partial x)(2x-8y+8xy) is 8y+2

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(\partial)/(\partial x)(2x-8y+8xy)

\frac{\partial}{\partial x} (2 x - 8 y + 8 x y)

8 y + 2

Solution steps

\frac{\partial}{\partial x} (2 x - 8 y + 8 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x) - \frac{\partial}{\partial x} (8 y) + \frac{\partial}{\partial x} (8 x y)

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (8 y) = 0

\frac{\partial}{\partial x} (8 x y) = 8 y

= 2 - 0 + 8 y

Simplify

= 8 y + 2

x^{4} + 5 y^{4} \frac{x ^{5} + 4 d y}{d x} = 0

(7, 2), (- 11, - 13)

\int \frac{1}{36 e ^{- 2 x} + e ^{2 x}} d x

\frac{d y}{d t} = - y

\frac{\partial}{\partial x} (cos (2 x) \cdot 2)

What is (\partial)/(\partial x)(2x-8y+8xy) ?
The answer to (\partial)/(\partial x)(2x-8y+8xy) is 8y+2