What is the derivative of ln(2x-x^2) ?

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

What is the first derivative of ln(2x-x^2) ?

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

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derivative of

ln (2 x - x^{2})

\frac{2 - 2 x}{2 x - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 - 2 x}{2 x - x ^{2}}

y = x, y = \frac{1}{x ^{2}}, x = 2

y^{^{'}} + \frac{2 y}{x} = - \frac{4}{x}, y (1) = 3

(\frac{1}{e ^{x}})^{^{'}}

\frac{d}{d x} (x + x + 8)

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

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