What is (\partial)/(\partial x)(9xe^{8xy}) ?

The answer to (\partial)/(\partial x)(9xe^{8xy}) is 9(e^{8xy}+8e^{8xy}xy)

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(\partial)/(\partial x)(9xe^{8xy})

\frac{\partial}{\partial x} (9 x e^{8 x y})

9 (e^{8 x y} + 8 e^{8 x y} x y)

Solution steps

\frac{\partial}{\partial x} (9 x e^{8 x y})

Treat

y

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (x e^{8 x y})

Apply the Product Rule:

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

f = x, g = e^{8 x y}

= 9 (\frac{\partial}{\partial x} (x) e^{8 x y} + \frac{\partial}{\partial x} (e^{8 x y}) x)

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

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

= 9 (1 \cdot e^{8 x y} + e^{8 x y} \cdot 8 y x)

Simplify

= 9 (e^{8 x y} + 8 e^{8 x y} x y)

\int x (x + 1)^{8} d x

\frac{d y}{d x} + y = x e^{5 x} y^{6}

\int_{- 2}^{2} (x + 5) d x

y^{^{'}} y^{^{''}} = 1

x \to 2 lim (2)

What is (\partial)/(\partial x)(9xe^{8xy}) ?
The answer to (\partial)/(\partial x)(9xe^{8xy}) is 9(e^{8xy}+8e^{8xy}xy)