What is the derivative of (x-1^{2x}) ?

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

What is the first derivative of (x-1^{2x}) ?

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

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\frac{d}{d 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{d}{d x} (10 arctan (x))

x \to - 2 lim (4 - x)

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

\int_{- 3}^{- 1} 2 x^{2} + 3 d x

e^{p} (p + p)

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