What is (\partial)/(\partial x)(y(-2x-y+1)) ?

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

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(\partial)/(\partial x)(y(-2x-y+1))

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

- 2 y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= y (- 2 - 0 + 0)

Simplify

= - 2 y

\frac{d}{d x} (e^{3 x - 1})

f (x) = \frac{1 - x}{2 x}, at x = 1

\frac{d}{d x} (\frac{1}{6} (x^{2} - 4)^{\frac{3}{2}})

\int \frac{5 - 50 x}{49 - 25 x ^{2}} d x

\frac{d}{d x} (e^{2 x} x + 1)

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