What is the derivative of 2e^{2x}*x ?

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

What is the first derivative of 2e^{2x}*x ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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