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

The answer to (\partial)/(\partial x)(7e^{x^7y}) is 49e^{x^7y}x^6y

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

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

49 e^{x^{7} y} x^{6} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{7} y) = 7 y x^{6}

= 7 e^{x^{7} y} \cdot 7 y x^{6}

Simplify

= 49 e^{x^{7} y} x^{6} y

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{6 x ^{\frac{5}{6}}})

\frac{\partial}{\partial x} (\frac{y + x y}{( 1 + x ) ^{3}})

\frac{d}{d x} (e^{5 x} \cdot 5)

u + 1 (1 - 8 u^{2})^{7}

e^{- b t}

What is (\partial)/(\partial x)(7e^{x^7y}) ?
The answer to (\partial)/(\partial x)(7e^{x^7y}) is 49e^{x^7y}x^6y