What is the derivative of ze^x(z+2) ?

The derivative of ze^x(z+2) is e^xz^2+2e^xz+2e^xz(dz)/(dx)+2e^x(dz)/(dx)

What is the first derivative of ze^x(z+2) ?

The first derivative of ze^x(z+2) is e^xz^2+2e^xz+2e^xz(dz)/(dx)+2e^x(dz)/(dx)

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

e^{x} z^{2} + 2 e^{x} z + 2 e^{x} z \frac{d z}{d x} + 2 e^{x} \frac{d z}{d x}

Solution steps

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

Apply the Product Rule:

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

f = z, g = e^{x} (z + 2)

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

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

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

Simplify

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

= e^{x} z^{2} + 2 e^{x} z + 2 e^{x} z \frac{d z}{d x} + 2 e^{x} \frac{d z}{d x}

2.5 \cdot 1 0^{- 12}

(1 + x^{2})^{2} \cdot (1 - 3 x)^{2}

6 (x^{2} + 4)^{2} (x - 4)^{2}

e^{- l n (2)}

3. 5^{2} e^{- 3.5}

What is the derivative of ze^x(z+2) ?
The derivative of ze^x(z+2) is e^xz^2+2e^xz+2e^xz(dz)/(dx)+2e^x(dz)/(dx)
What is the first derivative of ze^x(z+2) ?
The first derivative of ze^x(z+2) is e^xz^2+2e^xz+2e^xz(dz)/(dx)+2e^x(dz)/(dx)