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

The answer to (\partial)/(\partial x)(x^6e^{xy}) is 6x^5e^{xy}+e^{xy}yx^6

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(\partial)/(\partial x)(x^6e^{xy})

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{6}, g = e^{x y}

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

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

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

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

\frac{d ^{2}}{d x ^{2}} ((4 x^{2} + 9)^{6})

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

\int 2 x - 3 d x

\frac{\partial}{\partial x} (e^{x} + x cos (y))

\int \frac{x ^{2} - 1}{e ^{\frac{x}{2}}} d x

What is (\partial)/(\partial x)(x^6e^{xy}) ?
The answer to (\partial)/(\partial x)(x^6e^{xy}) is 6x^5e^{xy}+e^{xy}yx^6