What is the derivative of z^2ze^{xyz} ?

The derivative of z^2ze^{xyz} is e^{zxy}xyz^3+3z^2e^{zxy}

What is the first derivative of z^2ze^{xyz} ?

The first derivative of z^2ze^{xyz} is e^{zxy}xyz^3+3z^2e^{zxy}

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derivative of

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

e^{z x y} x y z^{3} + 3 z^{2} e^{z x y}

Solution steps

\frac{d}{d z} (z^{2} z e^{x yz})

Simplify

z^{2} z e^{x yz} : e^{z x y} z^{3}

= \frac{d}{d z} (e^{z x y} z^{3})

Treat

x, y

as constants

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{z x y}, g = z^{3}

= \frac{d}{d z} (e^{z x y}) z^{3} + \frac{d}{d z} (z^{3}) e^{z x y}

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

\frac{d}{d z} (z^{3}) = 3 z^{2}

= e^{z x y} x y z^{3} + 3 z^{2} e^{z x y}

\int tan^{3} (3 π x) d x

x \to 1 - lim (4 - x)

f (x) = x^{2} + 1, (3, 10)

f (x) = 30 x

f (x) = ln (\frac{x ^{2}}{x ^{2} + 4})

What is the derivative of z^2ze^{xyz} ?
The derivative of z^2ze^{xyz} is e^{zxy}xyz^3+3z^2e^{zxy}
What is the first derivative of z^2ze^{xyz} ?
The first derivative of z^2ze^{xyz} is e^{zxy}xyz^3+3z^2e^{zxy}