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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

y = \frac{ln ( x )}{e ^{x}}

\int csc (6 x) d x

\frac{2 s}{s ^{2} + 2 s + 1}

\int_{0}^{\frac{π}{4}} (sin (x)) d x

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

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