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

The answer to (\partial)/(\partial x)(8e^{x^8y}) is 64e^{x^8y}x^7y

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 8 \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}

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

Simplify

= 64 e^{x^{8} y} x^{7} y

\int \frac{sec ^{3} ( x )}{tan ^{4} ( x )} d x

\frac{d}{d y} (x^{2} + y^{2})

\frac{d}{d x} (\frac{x}{x + 10})

\int (\frac{x + 5}{x ^{2} + 11 x + 18}) d x

x \to 0 lim (1 + x)

What is (\partial)/(\partial x)(8e^{x^8y}) ?
The answer to (\partial)/(\partial x)(8e^{x^8y}) is 64e^{x^8y}x^7y