What is (\partial)/(\partial x)(8e^{x^6y}) ?

The answer to (\partial)/(\partial x)(8e^{x^6y}) is 48e^{x^6y}x^5y

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(\partial)/(\partial x)(8e^{x^6y})

\frac{\partial}{\partial x} (8 e^{x^{6} y})

48 e^{x^{6} y} x^{5} y

Solution steps

\frac{\partial}{\partial x} (8 e^{x^{6} y})

Treat

y

as a constant

Take the constant out:

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

= 8 \frac{\partial}{\partial x} (e^{x^{6} y})

Apply the chain rule:

e^{x^{6} y} \frac{\partial}{\partial x} (x^{6} y)

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

\frac{\partial}{\partial x} (x^{6} y) = 6 y x^{5}

= 8 e^{x^{6} y} \cdot 6 y x^{5}

Simplify

= 48 e^{x^{6} y} x^{5} y

\int x^{5} x^{6} + 8 d x

\int \frac{ln ( x )}{x ^{18}} d x

\int (x^{2} + 2) d x

\frac{\partial}{\partial y} (- cos (x y))

x \to 0 lim ((e^{x} - 1) ln (x))

What is (\partial)/(\partial x)(8e^{x^6y}) ?
The answer to (\partial)/(\partial x)(8e^{x^6y}) is 48e^{x^6y}x^5y