What is the derivative of e^{2x}(3x-2) ?

The derivative of e^{2x}(3x-2) is 6e^{2x}x-e^{2x}

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

The first derivative of e^{2x}(3x-2) is 6e^{2x}x-e^{2x}

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

6 e^{2 x} x - e^{2 x}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (3 x - 2) = 3

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

Simplify

e^{2 x} \cdot 2 (3 x - 2) + 3 e^{2 x} : 6 e^{2 x} x - e^{2 x}

= 6 e^{2 x} x - e^{2 x}

What is the derivative of e^{2x}(3x-2) ?
The derivative of e^{2x}(3x-2) is 6e^{2x}x-e^{2x}
What is the first derivative of e^{2x}(3x-2) ?
The first derivative of e^{2x}(3x-2) is 6e^{2x}x-e^{2x}