What is (\partial)/(\partial x)(y(-14x-4y+1)) ?

The answer to (\partial)/(\partial x)(y(-14x-4y+1)) is -14y

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(\partial)/(\partial x)(y(-14x-4y+1))

\frac{\partial}{\partial x} (y (- 14 x - 4 y + 1))

- 14 y

Solution steps

\frac{\partial}{\partial x} (y (- 14 x - 4 y + 1))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (- 14 x - 4 y + 1)

Apply the Sum/Difference Rule:

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

= y (- \frac{\partial}{\partial x} (14 x) - \frac{\partial}{\partial x} (4 y) + \frac{\partial}{\partial x} (1))

\frac{\partial}{\partial x} (14 x) = 14

\frac{\partial}{\partial x} (4 y) = 0

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

= y (- 14 - 0 + 0)

Simplify

= - 14 y

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

\int \frac{2}{x ^{\frac{1}{2}}} d x

2 x + 3 y + (6 x + 9 y - 3) y^{^{'}} = 0

f (x) = cos (x^{2}) - 2 x^{2} sin (x^{2})

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

What is (\partial)/(\partial x)(y(-14x-4y+1)) ?
The answer to (\partial)/(\partial x)(y(-14x-4y+1)) is -14y