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Popular >

derivative of e^{2x}(2x+1)

Solution

\frac{d}{d x} (e^{2 x} (2 x + 1))

Solution

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

Solution steps

\frac{d}{d x} (e^{2 x} (2 x + 1))

Apply the Product Rule:

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

f = e^{2 x}, g = 2 x + 1

= \frac{d}{d x} (e^{2 x}) (2 x + 1) + \frac{d}{d x} (2 x + 1) e^{2 x}

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

\frac{d}{d x} (2 x + 1) = 2

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}(2x+1) ?
The derivative of e^{2x}(2x+1) is 4e^{2x}x+4e^{2x}
What is the first derivative of e^{2x}(2x+1) ?
The first derivative of e^{2x}(2x+1) is 4e^{2x}x+4e^{2x}