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

The derivative of ln(2x+1)(e^x)^2 is 2e^{2x}ln(2x+1)+(2e^{2x})/(2x+1)

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

The first derivative of ln(2x+1)(e^x)^2 is 2e^{2x}ln(2x+1)+(2e^{2x})/(2x+1)

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derivative of

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

(1 - x^{2})^{10}

x^{3} y^{4}

y = sin (x^{2} + 2 x + 3)

\frac{d}{d b} (2 b)

\frac{d}{d o} (5^{c} os x)

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