What is the derivative of 5xe^{2x} ?

The derivative of 5xe^{2x} is 5(e^{2x}+2e^{2x}x)

What is the first derivative of 5xe^{2x} ?

The first derivative of 5xe^{2x} is 5(e^{2x}+2e^{2x}x)

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derivative of

5 x e^{2 x}

5 (e^{2 x} + 2 e^{2 x} x)

Solution steps

\frac{d}{d x} (5 x e^{2 x})

Take the constant out:

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

= 5 \frac{d}{d x} (x e^{2 x})

Apply the Product Rule:

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

f = x, g = e^{2 x}

= 5 (\frac{d x}{d x} e^{2 x} + \frac{d}{d x} (e^{2 x}) x)

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

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

= 5 (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x)

Simplify

= 5 (e^{2 x} + 2 e^{2 x} x)

What is the derivative of 5xe^{2x} ?
The derivative of 5xe^{2x} is 5(e^{2x}+2e^{2x}x)
What is the first derivative of 5xe^{2x} ?
The first derivative of 5xe^{2x} is 5(e^{2x}+2e^{2x}x)