What is the tangent of sqrt(x)+sqrt(y)=5 ?

The tangent of sqrt(x)+sqrt(y)=5 is y=(-5/(sqrt(a_{0))}+1)x-5sqrt(a_{0)}+25

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tangent of sqrt(x)+sqrt(y)=5

tangent of

x + y = 5

y = (- \frac{5}{a _{0}} + 1) x - 5 a_{0} + 25

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 25 - 10 a_{0} + a_{0})

Find the slope of

x + y = 5 : \frac{d y}{d x} = - \frac{5}{x} + 1

Compute the slope of

x + y = 5

x = a_{0} : m = - \frac{5}{a _{0}} + 1

Find the line with slope m=

- \frac{5}{a _{0}} + 1

and passing through

(a_{0}, 25 - 10 a_{0} + a_{0}) : y = (- \frac{5}{a _{0}} + 1) x - 5 a_{0} + 25

y = (- \frac{5}{a _{0}} + 1) x - 5 a_{0} + 25

\int 2 sin (x) - cos (x) d x

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

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

k = 0 \sum \infty \frac{x ^{k}}{k !}

- cos (x), cos^{2} (x), [\frac{- π}{2}, \frac{π}{2}]

What is the tangent of sqrt(x)+sqrt(y)=5 ?
The tangent of sqrt(x)+sqrt(y)=5 is y=(-5/(sqrt(a_{0))}+1)x-5sqrt(a_{0)}+25