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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

x \to 0 + lim (x e^{- \frac{2}{x}})

y^{^{'}} + 2 t y = e^{- t^{2}}

\int_{0}^{π} 6 cos^{2} (3 x) d x

\int (x^{2} - 4 x + 5)^{2} d x

(x + 2)^{\frac{2}{3}}

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