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

The answer to (\partial)/(\partial x)(5e^{x^5y}) is 25e^{x^5y}x^4y

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

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

25 e^{x^{5} y} x^{4} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{5} y) = 5 y x^{4}

= 5 e^{x^{5} y} \cdot 5 y x^{4}

Simplify

= 25 e^{x^{5} y} x^{4} y

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What is (\partial)/(\partial x)(5e^{x^5y}) ?
The answer to (\partial)/(\partial x)(5e^{x^5y}) is 25e^{x^5y}x^4y