What is (\partial)/(\partial z)(e^{xyz^2+z}) ?

The answer to (\partial)/(\partial z)(e^{xyz^2+z}) is e^{xyz^2+z}(2xyz+1)

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(\partial)/(\partial z)(e^{xyz^2+z})

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

e^{x y z^{2} + z} (2 x yz + 1)

Solution steps

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

Treat

x, y

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial z} (x y z^{2} + z) = 2 x yz + 1

= e^{x y z^{2} + z} (2 x yz + 1)

\frac{\partial}{\partial x} (4 x^{2} + 4 y^{3})

\int (3 x^{2} + 4) x - 1 d x

\int_{4}^{7} (x - 5)^{2} d x

y^{^{'}} + y = e^{x}, y (0) = 6

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{5}})

What is (\partial)/(\partial z)(e^{xyz^2+z}) ?
The answer to (\partial)/(\partial z)(e^{xyz^2+z}) is e^{xyz^2+z}(2xyz+1)