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

The derivative of (x^2+3xe^{2x}) is 2e^{2x}x^2+8e^{2x}x+3e^{2x}

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

The first derivative of (x^2+3xe^{2x}) is 2e^{2x}x^2+8e^{2x}x+3e^{2x}

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

2 e^{2 x} x^{2} + 8 e^{2 x} x + 3 e^{2 x}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + 3 x, g = e^{2 x}

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

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

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

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

Simplify

(2 x + 3) e^{2 x} + e^{2 x} \cdot 2 (x^{2} + 3 x) : 2 e^{2 x} x^{2} + 8 e^{2 x} x + 3 e^{2 x}

= 2 e^{2 x} x^{2} + 8 e^{2 x} x + 3 e^{2 x}

4 t^{3}

x \to \infty + lim (4 x)

[x + (x + sin^{2} (x))^{3}]^{6}

\int x e^{y x} d x

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

What is the derivative of (x^2+3xe^{2x}) ?
The derivative of (x^2+3xe^{2x}) is 2e^{2x}x^2+8e^{2x}x+3e^{2x}
What is the first derivative of (x^2+3xe^{2x}) ?
The first derivative of (x^2+3xe^{2x}) is 2e^{2x}x^2+8e^{2x}x+3e^{2x}