What is (\partial)/(\partial x)(9xe^{6xy}) ?

The answer to (\partial)/(\partial x)(9xe^{6xy}) is 9(e^{6xy}+6e^{6xy}xy)

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(\partial)/(\partial x)(9xe^{6xy})

\frac{\partial}{\partial x} (9 x e^{6 x y})

9 (e^{6 x y} + 6 e^{6 x y} x y)

Solution steps

\frac{\partial}{\partial x} (9 x e^{6 x y})

Treat

y

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (x e^{6 x y})

Apply the Product Rule:

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

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

= 9 (\frac{\partial}{\partial x} (x) e^{6 x y} + \frac{\partial}{\partial x} (e^{6 x y}) x)

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

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

= 9 (1 \cdot e^{6 x y} + e^{6 x y} \cdot 6 y x)

Simplify

= 9 (e^{6 x y} + 6 e^{6 x y} x y)

What is (\partial)/(\partial x)(9xe^{6xy}) ?
The answer to (\partial)/(\partial x)(9xe^{6xy}) is 9(e^{6xy}+6e^{6xy}xy)