What is the derivative of 7(2ze^z+e^zz^2) ?

The derivative of 7(2ze^z+e^zz^2) is 7(e^zz^2+4e^zz+2e^z)

What is the first derivative of 7(2ze^z+e^zz^2) ?

The first derivative of 7(2ze^z+e^zz^2) is 7(e^zz^2+4e^zz+2e^z)

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derivative of

7 (2 z e^{z} + e^{z} z^{2})

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

Solution steps

\frac{d}{d z} (7 (2 z e^{z} + e^{z} z^{2}))

Take the constant out:

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

= 7 \frac{d}{d z} (2 z e^{z} + e^{z} z^{2})

Apply the Sum/Difference Rule:

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

= 7 (\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}

= 7 (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}

= 7 (e^{z} z^{2} + 4 e^{z} z + 2 e^{z})

f (x) = arcsin (1 - x^{2})

x^{^{''}} + 9 x = 27

\int \frac{1}{2} e^{π x i (n - m)} d x

\frac{9}{s ( s + 3 ) ^{2}}

\frac{d}{d x} (- 3 sin (sin (3 x)) cos (3 x))

What is the derivative of 7(2ze^z+e^zz^2) ?
The derivative of 7(2ze^z+e^zz^2) is 7(e^zz^2+4e^zz+2e^z)
What is the first derivative of 7(2ze^z+e^zz^2) ?
The first derivative of 7(2ze^z+e^zz^2) is 7(e^zz^2+4e^zz+2e^z)