What is (\partial)/(\partial x)(xe^{9xy}) ?

The answer to (\partial)/(\partial x)(xe^{9xy}) is e^{9xy}+9e^{9xy}xy

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(\partial)/(\partial x)(xe^{9xy})

\frac{\partial}{\partial x} (x e^{9 x y})

e^{9 x y} + 9 e^{9 x y} x y

Solution steps

\frac{\partial}{\partial x} (x e^{9 x y})

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = e^{9 x y}

= \frac{\partial}{\partial x} (x) e^{9 x y} + \frac{\partial}{\partial x} (e^{9 x y}) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{9 x y}) = e^{9 x y} \cdot 9 y

= 1 \cdot e^{9 x y} + e^{9 x y} \cdot 9 y x

Simplify

= e^{9 x y} + 9 e^{9 x y} x y

\int_{4}^{10} 6 d x

\int k e^{- k^{2}}

\frac{d}{d x} (10 + (\frac{50 x}{2 x ^{2} + 9}))

x \to 0 - lim (\frac{6}{x} - \frac{6}{∣ x ∣})

x \cdot y^{^{'}} + y = x^{4} \cdot y^{3}

What is (\partial)/(\partial x)(xe^{9xy}) ?
The answer to (\partial)/(\partial x)(xe^{9xy}) is e^{9xy}+9e^{9xy}xy