What is (\partial)/(\partial x)(6y-5x^2e^{5y}) ?

The answer to (\partial)/(\partial x)(6y-5x^2e^{5y}) is -10e^{5y}x

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(\partial)/(\partial x)(6y-5x^2e^{5y})

\frac{\partial}{\partial x} (6 y - 5 x^{2} e^{5 y})

- 10 e^{5 y} x

Solution steps

\frac{\partial}{\partial x} (6 y - 5 x^{2} e^{5 y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 y) - \frac{\partial}{\partial x} (5 x^{2} e^{5 y})

\frac{\partial}{\partial x} (6 y) = 0

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

= 0 - 10 e^{5 y} x

Simplify

= - 10 e^{5 y} x

What is (\partial)/(\partial x)(6y-5x^2e^{5y}) ?
The answer to (\partial)/(\partial x)(6y-5x^2e^{5y}) is -10e^{5y}x