What is the derivative of f(z)=8z^2e^z ?

The derivative of f(z)=8z^2e^z is 8(2ze^z+e^zz^2)

What is the first derivative of f(z)=8z^2e^z ?

The first derivative of f(z)=8z^2e^z is 8(2ze^z+e^zz^2)

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derivative of

f (z) = 8 z^{2} e^{z}

8 (2 z e^{z} + e^{z} z^{2})

Solution steps

\frac{d}{d z} (8 z^{2} e^{z})

Take the constant out:

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

= 8 \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}

= 8 (\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}

= 8 (2 z e^{z} + e^{z} z^{2})

x + 5

\frac{d ^{4} y}{d x ^{4}} - 3 y = 0

y = x, y = ln (x), x = 1, x = 2

\frac{d}{d x} (\frac{1}{1 + 3 x})

\int_{1}^{e} ln (x^{2}) d x

What is the derivative of f(z)=8z^2e^z ?
The derivative of f(z)=8z^2e^z is 8(2ze^z+e^zz^2)
What is the first derivative of f(z)=8z^2e^z ?
The first derivative of f(z)=8z^2e^z is 8(2ze^z+e^zz^2)