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

The derivative of e^{2x}x is 2e^{2x}x+e^{2x}

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

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

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

2 e^{2 x} x + e^{2 x}

Solution steps

\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

= \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

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

Simplify

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

(2, - 4), (6, 0)

\frac{\partial}{\partial x} (2 x cos (x^{2} + y^{2}))

x \to - 3 + lim (\frac{x ^{2} - 9}{x + 3})

x y + y^{^{'}} = 142 x

\frac{d y}{d x} = 2 x - 1 + 2 x y - y

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