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Popular >

derivative of 2e^{2x}x

Solution

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

Solution

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})

Popular Examples

integral of e^{3x+1}

\int e^{3 x + 1} d x

integral from 2 to 6 of 1/(x^2-1)

\int_{2}^{6} \frac{1}{x ^{2} - 1} d x

(\partial)/(\partial y)(e^{y^2})

\frac{\partial}{\partial y} (e^{y^{2}})

t*(dy)/(dt)=t^3+25t^3y

t \cdot \frac{d y}{d t} = t^{3} + 25 t^{3} y

derivative of (e^{x^2}/x)

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

Frequently Asked Questions (FAQ)

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})