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Popular >

derivative of 2xe^{2x}

Solution

derivative of

2 x e^{2 x}

Solution

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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

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

Simplify

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

Popular Examples

sum from n=9 to infinity of e^{7-4n}

n = 9 \sum \infty e^{7 - 4 n}

(\partial)/(\partial x)(e^{7x+7y})

\frac{\partial}{\partial x} (e^{7 x + 7 y})

limit as x approaches-5 of (x+5)/(5-|x|)

x \to - 5 lim (\frac{x + 5}{5 - ∣ x ∣})

integral of (x^2-1)^5(2x)

\int (x^{2} - 1)^{5} (2 x) d x

limit as t approaches-2 of sqrt(8+t^3)

t \to - 2 lim (8 + t^{3})

Frequently Asked Questions (FAQ)

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