What is (\partial)/(\partial x)(7e^{x^5y}) ?

The answer to (\partial)/(\partial x)(7e^{x^5y}) is 35e^{x^5y}x^4y

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(\partial)/(\partial x)(7e^{x^5y})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 7 \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}

= 7 e^{x^{5} y} \cdot 5 y x^{4}

Simplify

= 35 e^{x^{5} y} x^{4} y

\int_{- 1}^{1} \frac{1}{x ^{2} - 2 x} d x

n = 1 \sum \infty \frac{2}{n} - \frac{2}{n + 1}

\int \frac{x ^{2}}{( 1 - x ^{2} ) ^{\frac{5}{2}}} d x

\frac{e ^{- 2 s}}{s ^{2}}

x \to - 2 lim (8)

What is (\partial)/(\partial x)(7e^{x^5y}) ?
The answer to (\partial)/(\partial x)(7e^{x^5y}) is 35e^{x^5y}x^4y