What is (\partial)/(\partial x)(y^2-4x^2+7y+5x+13) ?

The answer to (\partial)/(\partial x)(y^2-4x^2+7y+5x+13) is -8x+5

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(\partial)/(\partial x)(y^2-4x^2+7y+5x+13)

\frac{\partial}{\partial x} (y^{2} - 4 x^{2} + 7 y + 5 x + 13)

- 8 x + 5

Solution steps

\frac{\partial}{\partial x} (y^{2} - 4 x^{2} + 7 y + 5 x + 13)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (7 y) + \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (13)

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (7 y) = 0

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

\frac{\partial}{\partial x} (13) = 0

= 0 - 8 x + 0 + 5 + 0

Simplify

= - 8 x + 5

y^{^{'}} + 5 (cos (5 x)) y = - 8 cos (5 x)

y^{2} = 4 x, y^{2} = 8 x - 4, x

x \to 42 lim (\frac{x ^{2}}{6} - \frac{7}{x})

\frac{1 + 10 s}{s ^{2} + 10.1 s + 1}

What is (\partial)/(\partial x)(y^2-4x^2+7y+5x+13) ?
The answer to (\partial)/(\partial x)(y^2-4x^2+7y+5x+13) is -8x+5