What is (\partial)/(\partial x)(z*e^{xyz}) ?

The answer to (\partial)/(\partial x)(z*e^{xyz}) is e^{zxy}z^2y

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(\partial)/(\partial x)(z*e^{xyz})

\frac{\partial}{\partial x} (z \cdot e^{x yz})

e^{z x y} z^{2} y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

e^{x yz} \frac{\partial}{\partial x} (x yz)

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

\frac{\partial}{\partial x} (x yz) = zy

= z e^{x yz} zy

Simplify

z e^{x yz} zy : e^{z x y} z^{2} y

= e^{z x y} z^{2} y

y^{^{'}} = 6 x y^{2}

\frac{d}{d x} (x^{3} (x - 5)^{2})

h \to \infty lim (\frac{5 h ^{4} - 2 h ^{2} + 3}{3 h ^{3} + 2 h ^{2} + h})

\int (x^{2} + y^{2})^{(- \frac{3}{2})} d y

\frac{d y}{d x} = 2 x (1 + y) e^{x^{2}}

What is (\partial)/(\partial x)(z*e^{xyz}) ?
The answer to (\partial)/(\partial x)(z*e^{xyz}) is e^{zxy}z^2y