What is the tangent of sqrt(1-2x) ?

The tangent of sqrt(1-2x) is y=-1/(sqrt(1-2a_{0))}x+sqrt(1-2a_{0)}+(a_{0})/(sqrt(1-2a_{0))}

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tangent of sqrt(1-2x)

tangent of

1 - 2 x

y = - \frac{1}{1 - 2 a _{0}} x + 1 - 2 a_{0} + \frac{a _{0}}{1 - 2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 1 - 2 a_{0})

Find the slope of

y = 1 - 2 x : \frac{d y}{d x} = - \frac{1}{1 - 2 x}

Compute the slope of

y = 1 - 2 x

x = a_{0} : m = - \frac{1}{1 - 2 a _{0}}

Find the line with slope m=

- \frac{1}{1 - 2 a _{0}}

and passing through

(a_{0}, 1 - 2 a_{0}) : y = - \frac{1}{1 - 2 a _{0}} x + 1 - 2 a_{0} + \frac{a _{0}}{1 - 2 a _{0}}

y = - \frac{1}{1 - 2 a _{0}} x + 1 - 2 a_{0} + \frac{a _{0}}{1 - 2 a _{0}}

n = 1 \sum \infty \frac{2 n}{n !}

\int \frac{6 x ^{3} + 2 x ^{2} - 47 x - 9}{x ^{2} - 9} d x

f (x) = 7 x - 2 x^{2}, (- 1, - 9)

\int (2 x + 7)^{2} d x

\int \frac{1}{1 - sin ( 2 x )} d x

What is the tangent of sqrt(1-2x) ?
The tangent of sqrt(1-2x) is y=-1/(sqrt(1-2a_{0))}x+sqrt(1-2a_{0)}+(a_{0})/(sqrt(1-2a_{0))}