What is (\partial)/(\partial x)(7e^{x^8y}) ?

The answer to (\partial)/(\partial x)(7e^{x^8y}) is 56e^{x^8y}x^7y

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(\partial)/(\partial x)(7e^{x^8y})

\frac{\partial}{\partial x} (7 e^{x^{8} y})

56 e^{x^{8} y} x^{7} y

Solution steps

\frac{\partial}{\partial x} (7 e^{x^{8} y})

Treat

y

as a constant

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (e^{x^{8} y})

Apply the chain rule:

e^{x^{8} y} \frac{\partial}{\partial x} (x^{8} y)

= e^{x^{8} y} \frac{\partial}{\partial x} (x^{8} y)

\frac{\partial}{\partial x} (x^{8} y) = 8 y x^{7}

= 7 e^{x^{8} y} \cdot 8 y x^{7}

Simplify

= 56 e^{x^{8} y} x^{7} y

What is (\partial)/(\partial x)(7e^{x^8y}) ?
The answer to (\partial)/(\partial x)(7e^{x^8y}) is 56e^{x^8y}x^7y