What is (\partial)/(\partial x)(xye^{4x-2z}) ?

The answer to (\partial)/(\partial x)(xye^{4x-2z}) is y(e^{4x-2z}+4e^{4x-2z}x)

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(\partial)/(\partial x)(xye^{4x-2z})

\frac{\partial}{\partial x} (x y e^{4 x - 2 z})

y (e^{4 x - 2 z} + 4 e^{4 x - 2 z} x)

Solution steps

\frac{\partial}{\partial x} (x y e^{4 x - 2 z})

Treat

y, z

as constants

Take the constant out:

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

= y \frac{\partial}{\partial x} (x e^{4 x - 2 z})

Apply the Product Rule:

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

f = x, g = e^{4 x - 2 z}

= y (\frac{\partial}{\partial x} (x) e^{4 x - 2 z} + \frac{\partial}{\partial x} (e^{4 x - 2 z}) x)

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

\frac{\partial}{\partial x} (e^{4 x - 2 z}) = e^{4 x - 2 z} \cdot 4

= y (1 \cdot e^{4 x - 2 z} + e^{4 x - 2 z} \cdot 4 x)

Simplify

= y (e^{4 x - 2 z} + 4 e^{4 x - 2 z} x)

\frac{d y}{d x} + 9 y = e^{8 x}

x^{2}

- x, x^{2} - 12

n = 0 \sum \infty \frac{1}{13 n + 42}

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

What is (\partial)/(\partial x)(xye^{4x-2z}) ?
The answer to (\partial)/(\partial x)(xye^{4x-2z}) is y(e^{4x-2z}+4e^{4x-2z}x)