What is the derivative of 3xe^{2x} ?

The derivative of 3xe^{2x} is 3(e^{2x}+2e^{2x}x)

What is the first derivative of 3xe^{2x} ?

The first derivative of 3xe^{2x} is 3(e^{2x}+2e^{2x}x)

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derivative of

3 x e^{2 x}

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

Solution steps

\frac{d}{d x} (3 x e^{2 x})

Take the constant out:

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

= 3 \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}

= 3 (\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

= 3 (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x)

Simplify

= 3 (e^{2 x} + 2 e^{2 x} x)

t^{2} \frac{d y}{d t} + t y = 3

\frac{d}{d t} (5 t + \frac{7}{t})

ln (x), 1, - 1

y = x^{2} + 5 x, x = 4

\frac{\partial}{\partial x} (7 + x^{2} + y^{2})

What is the derivative of 3xe^{2x} ?
The derivative of 3xe^{2x} is 3(e^{2x}+2e^{2x}x)
What is the first derivative of 3xe^{2x} ?
The first derivative of 3xe^{2x} is 3(e^{2x}+2e^{2x}x)