What is the d/(dz)(z^2e^z) ?

The d/(dz)(z^2e^z) is 2ze^z+e^zz^2

What is the first d/(dz)(z^2e^z) ?

The first d/(dz)(z^2e^z) is 2ze^z+e^zz^2

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

2 z e^{z} + e^{z} z^{2}

Solution steps

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

Apply the Product Rule:

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

f = z^{2}, g = e^{z}

= \frac{d}{d z} (z^{2}) e^{z} + \frac{d}{d z} (e^{z}) z^{2}

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

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

= 2 z e^{z} + e^{z} z^{2}

f (x) = \frac{1}{( 1 + x )}

\frac{d}{d x} (4 ln ∣ x - e^{x} ∣)

y = \frac{cos ( x )}{1 - sin ( x )}

y = cos (sin (tan (9 x)))

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