What is (\partial)/(\partial x)(x^5e^{xy}+3x) ?

The answer to (\partial)/(\partial x)(x^5e^{xy}+3x) is 5x^4e^{xy}+e^{xy}yx^5+3

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(\partial)/(\partial x)(x^5e^{xy}+3x)

\frac{\partial}{\partial x} (x^{5} e^{x y} + 3 x)

5 x^{4} e^{x y} + e^{x y} y x^{5} + 3

Solution steps

\frac{\partial}{\partial x} (x^{5} e^{x y} + 3 x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{5} e^{x y}) + \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (x^{5} e^{x y}) = 5 x^{4} e^{x y} + e^{x y} y x^{5}

\frac{\partial}{\partial x} (3 x) = 3

= 5 x^{4} e^{x y} + e^{x y} y x^{5} + 3

\frac{3}{8 x ^{\frac{5}{2}}}

\frac{d}{d x} (4 x y^{3})

x (9.3)

y^{^{'}} = - \frac{y}{t} + 2

f (x) = x^{4} - 4 x^{2}, g (x) = x^{2} - 4

What is (\partial)/(\partial x)(x^5e^{xy}+3x) ?
The answer to (\partial)/(\partial x)(x^5e^{xy}+3x) is 5x^4e^{xy}+e^{xy}yx^5+3