What is the derivative of 3(2ze^z+e^zz^2) ?

The derivative of 3(2ze^z+e^zz^2) is 3(e^zz^2+4e^zz+2e^z)

What is the first derivative of 3(2ze^z+e^zz^2) ?

The first derivative of 3(2ze^z+e^zz^2) is 3(e^zz^2+4e^zz+2e^z)

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derivative of

3 (2 z e^{z} + e^{z} z^{2})

3 (e^{z} z^{2} + 4 e^{z} z + 2 e^{z})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 3 (2 (e^{z} + e^{z} z) + e^{z} z^{2} + 2 z e^{z})

Expand

2 (e^{z} + e^{z} z) + e^{z} z^{2} + 2 z e^{z} : e^{z} z^{2} + 4 e^{z} z + 2 e^{z}

= 3 (e^{z} z^{2} + 4 e^{z} z + 2 e^{z})

f (x) = (x - 4)^{2}

\frac{d}{d x} (ln (e^{15 x}))

9 + 5 x^{2}

\int_{0}^{R} \frac{1}{1 + x ^{2}} d x

\int sin (2 x) - cos (2 x) d x

What is the derivative of 3(2ze^z+e^zz^2) ?
The derivative of 3(2ze^z+e^zz^2) is 3(e^zz^2+4e^zz+2e^z)
What is the first derivative of 3(2ze^z+e^zz^2) ?
The first derivative of 3(2ze^z+e^zz^2) is 3(e^zz^2+4e^zz+2e^z)