What is (\partial)/(\partial z)(-ye^{z^3+z^2+1}) ?

The answer to (\partial)/(\partial z)(-ye^{z^3+z^2+1}) is -ye^{z^3+z^2+1}(3z^2+2z)

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(\partial)/(\partial z)(-ye^{z^3+z^2+1})

\frac{\partial}{\partial z} (- y e^{z^{3} + z^{2} + 1})

- y e^{z^{3} + z^{2} + 1} (3 z^{2} + 2 z)

Solution steps

\frac{\partial}{\partial z} (- y e^{z^{3} + z^{2} + 1})

Treat

y

as a constant

Take the constant out:

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

= - y \frac{\partial}{\partial z} (e^{z^{3} + z^{2} + 1})

Apply the chain rule:

e^{z^{3} + z^{2} + 1} \frac{\partial}{\partial z} (z^{3} + z^{2} + 1)

= e^{z^{3} + z^{2} + 1} \frac{\partial}{\partial z} (z^{3} + z^{2} + 1)

\frac{\partial}{\partial z} (z^{3} + z^{2} + 1) = 3 z^{2} + 2 z

= - y e^{z^{3} + z^{2} + 1} (3 z^{2} + 2 z)

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What is (\partial)/(\partial z)(-ye^{z^3+z^2+1}) ?
The answer to (\partial)/(\partial z)(-ye^{z^3+z^2+1}) is -ye^{z^3+z^2+1}(3z^2+2z)