What is the derivative of e^x(2x+1) ?

The derivative of e^x(2x+1) is 2e^xx+3e^x

What is the first derivative of e^x(2x+1) ?

The first derivative of e^x(2x+1) is 2e^xx+3e^x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

e^{x} (2 x + 1) + 2 e^{x} : 2 e^{x} x + 3 e^{x}

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

\frac{d y}{d x} = 9 + 3 x

\frac{d}{d y} (arcsin (y))

\int x n x d x

sin (θ) + cos (θ) θ

\int \frac{x ^{2}}{1 - x} d x

What is the derivative of e^x(2x+1) ?
The derivative of e^x(2x+1) is 2e^xx+3e^x
What is the first derivative of e^x(2x+1) ?
The first derivative of e^x(2x+1) is 2e^xx+3e^x