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

The answer to (\partial)/(\partial x)(-5x^2+7y^5x) is -10x+7y^5

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

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

- 10 x + 7 y^{5}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

= - 10 x + 7 y^{5}

What is (\partial)/(\partial x)(-5x^2+7y^5x) ?
The answer to (\partial)/(\partial x)(-5x^2+7y^5x) is -10x+7y^5