What is the derivative of 4xe^{2x} ?

The derivative of 4xe^{2x} is 4(e^{2x}+2e^{2x}x)

What is the first derivative of 4xe^{2x} ?

The first derivative of 4xe^{2x} is 4(e^{2x}+2e^{2x}x)

Popular >

\frac{d}{d x} (4 x e^{2 x})

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

Solution steps

\frac{d}{d x} (4 x e^{2 x})

Take the constant out:

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

= 4 \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}

= 4 (\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

= 4 (1 \cdot e^{2 x} + e^{2 x} \cdot 2 x)

Simplify

= 4 (e^{2 x} + 2 e^{2 x} x)

\frac{d}{d x} (x, y)

x \to 0 lim (\frac{( x ^{2} + 1 )}{x})

\int_{0}^{1} x^{4} + 2 x^{2} + 1 d x

\int x (3 + \frac{2}{x})^{2} d x

\int p (p + 9)^{7} d p

What is the derivative of 4xe^{2x} ?
The derivative of 4xe^{2x} is 4(e^{2x}+2e^{2x}x)
What is the first derivative of 4xe^{2x} ?
The first derivative of 4xe^{2x} is 4(e^{2x}+2e^{2x}x)