What is (\partial)/(\partial x)(6xye^{xz}) ?

The answer to (\partial)/(\partial x)(6xye^{xz}) is 6y(e^{xz}+e^{xz}xz)

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(\partial)/(\partial x)(6xye^{xz})

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{x z}

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

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

\frac{\partial}{\partial x} (e^{x z}) = e^{x z} z

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

Simplify

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

x \to 0 lim (\frac{tan ( \frac{x}{3} )}{x})

x^{2} - 8 x

\frac{d v}{d x} + 10 v = 5 x

f (x) = 2 sin (x), g (x) = tan (x)

\int \frac{sin ( t )}{t} d t

What is (\partial)/(\partial x)(6xye^{xz}) ?
The answer to (\partial)/(\partial x)(6xye^{xz}) is 6y(e^{xz}+e^{xz}xz)