What is (\partial)/(\partial y)(ze^{xyz}) ?

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

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(\partial)/(\partial y)(ze^{xyz})

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

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

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x yz) = z x

= z e^{x yz} z x

Simplify

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

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

x \to 4 + lim (\frac{1}{( x + 4 ) ^{3}})

\int (\frac{1}{cos ^{2} ( x )}) d x

\frac{\partial}{\partial x} (15 - 5 (x + 3)^{2})

\int (y - y) d y

\int \frac{1}{cosh ( x )} d x

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