What is the derivative of (x+1e^{{z}(x)}) ?

The derivative of (x+1e^{{z}(x)}) is e^{{z}(x)}+e^{{z}(x)} derivative of {z}(x)(x+1)

What is the first derivative of (x+1e^{{z}(x)}) ?

The first derivative of (x+1e^{{z}(x)}) is e^{{z}(x)}+e^{{z}(x)} derivative of {z}(x)(x+1)

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\frac{d}{d x} ((x + 1) e^{z (x)})

e^{z (x)} + e^{z (x)} \frac{d}{d x} (z (x)) (x + 1)

Solution steps

\frac{d}{d x} ((x + 1) e^{z (x)})

Apply the Product Rule:

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

f = x + 1, g = e^{z (x)}

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

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

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

= 1 \cdot e^{z (x)} + e^{z (x)} \frac{d}{d x} (z (x)) (x + 1)

Simplify

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

x \to - 5 lim (- x^{2} + 2 x - 5)

\frac{d}{d x} (49 - x^{2})

\frac{1}{4} x^{4} - \frac{2}{3} x^{3} + 2

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

\int_{1}^{\infty} \frac{x}{x ^{2} + 2} d x

What is the derivative of (x+1e^{{z}(x)}) ?
The derivative of (x+1e^{{z}(x)}) is e^{{z}(x)}+e^{{z}(x)} derivative of {z}(x)(x+1)
What is the first derivative of (x+1e^{{z}(x)}) ?
The first derivative of (x+1e^{{z}(x)}) is e^{{z}(x)}+e^{{z}(x)} derivative of {z}(x)(x+1)