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)

\int_{0}^{\frac{π}{4}} sin^{5} (2 x) d x

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

x \to \infty lim \frac{( ( a ^{(\frac{1}{x})} + b ^{(\frac{1}{x})} ) ^{x} )}{2 ^{x}}

y^{^{'}} + 10 (tan (10 x)) y = 9 cos (10 x)

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

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)