What is the tangent of f(x)=(x^{1/2})/(x+9),\at x=1 ?

The tangent of f(x)=(x^{1/2})/(x+9),\at x=1 is y= 1/25 x+3/50

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tangent of f(x)=(x^{1/2})/(x+9),\at x=1

tangent of

f (x) = \frac{x ^{\frac{1}{2}}}{x + 9}, at x = 1

y = \frac{1}{25} x + \frac{3}{50}

Solution steps

Find the tangent point:

(1, \frac{1}{10})

Find the slope of

f (x) = \frac{x ^{\frac{1}{2}}}{x + 9} : \frac{df ( x )}{d x} = \frac{- x + 9}{2 x ^{\frac{1}{2}} ( x + 9 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{25}

Find the line with slope m=

\frac{1}{25}

and passing through

(1, \frac{1}{10}) : y = \frac{1}{25} x + \frac{3}{50}

y = \frac{1}{25} x + \frac{3}{50}

x d y - y d x + y^{2} d x = 0

\frac{d}{d x} (4 sinh (2 x))

\frac{\partial}{\partial y} (e^{1 - x y})

x \to 1 - lim (\frac{1}{x + 1})

\int_{- π}^{π} t sin (n t) d t

What is the tangent of f(x)=(x^{1/2})/(x+9),\at x=1 ?
The tangent of f(x)=(x^{1/2})/(x+9),\at x=1 is y= 1/25 x+3/50