What is the derivative of (z^2+e^z)sqrt(z) ?

The derivative of (z^2+e^z)sqrt(z) is (5z^2+2e^zz+e^z)/(2sqrt(z))

What is the first derivative of (z^2+e^z)sqrt(z) ?

The first derivative of (z^2+e^z)sqrt(z) is (5z^2+2e^zz+e^z)/(2sqrt(z))

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derivative of

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

\frac{5 z ^{2} + 2 e ^{z} z + e ^{z}}{2 z}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d z} (z) = \frac{1}{2 z}

= (2 z + e^{z}) z + \frac{1}{2 z} (z^{2} + e^{z})

Simplify

(2 z + e^{z}) z + \frac{1}{2 z} (z^{2} + e^{z}) : \frac{5 z ^{2} + 2 e ^{z} z + e ^{z}}{2 z}

= \frac{5 z ^{2} + 2 e ^{z} z + e ^{z}}{2 z}

\frac{d y}{d x} = - 2 y + x, y (0) = 0

\frac{d}{d x} (x + x^{2})

\int t^{5} d t

\frac{1}{s ( s + 4 ) ^{2}}

\frac{d}{d x} ((3 x^{2} + 5)^{3} (3 x - 1)^{2})

What is the derivative of (z^2+e^z)sqrt(z) ?
The derivative of (z^2+e^z)sqrt(z) is (5z^2+2e^zz+e^z)/(2sqrt(z))
What is the first derivative of (z^2+e^z)sqrt(z) ?
The first derivative of (z^2+e^z)sqrt(z) is (5z^2+2e^zz+e^z)/(2sqrt(z))