What is the derivative of f(x)=(x+1)^{2x} ?

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

What is the first derivative of f(x)=(x+1)^{2x} ?

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

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

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

Apply the chain rule:

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

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

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

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

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

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

\frac{x}{a}

\frac{x}{y} = sin (\frac{π x y}{2}), (1, 1)

\frac{\partial}{\partial x} (y^{2} + 2 x y - x^{2})

x \to 16 lim (x + 2 x)

y = x \cdot x

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