What is the derivative of xe^{3{z}(x}) ?

The derivative of xe^{3{z}(x}) is e^{3{z}(x)}+3e^{3{z}(x)}x derivative of {z}(x)

What is the first derivative of xe^{3{z}(x}) ?

The first derivative of xe^{3{z}(x}) is e^{3{z}(x)}+3e^{3{z}(x)}x derivative of {z}(x)

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\frac{d}{d x} (x e^{3 z (x)})

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

Solution steps

\frac{d}{d x} (x e^{3 z (x)})

Apply the Product Rule:

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

f = x, g = e^{3 z (x)}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{3 z (x)}) = e^{3 z (x)} \cdot 3 \frac{d}{d x} (z (x))

= 1 \cdot e^{3 z (x)} + e^{3 z (x)} \cdot 3 \frac{d}{d x} (z (x)) x

Simplify

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

f (x) = x^{3} + \frac{2}{x}, at x = 1

δ (t)

y^{^{'}} - 2 y = 5

\int \frac{ln ( 6 x )}{x} d x

\int_{6}^{9} (x - 7)^{2} d x

What is the derivative of xe^{3{z}(x}) ?
The derivative of xe^{3{z}(x}) is e^{3{z}(x)}+3e^{3{z}(x)}x derivative of {z}(x)
What is the first derivative of xe^{3{z}(x}) ?
The first derivative of xe^{3{z}(x}) is e^{3{z}(x)}+3e^{3{z}(x)}x derivative of {z}(x)