What is the tangent of y=(2x)/(x+5),(5,1) ?

The tangent of y=(2x)/(x+5),(5,1) is y= 1/10 x+1/2

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tangent of y=(2x)/(x+5),(5,1)

tangent of

y = \frac{2 x}{x + 5}, (5, 1)

y = \frac{1}{10} x + \frac{1}{2}

Solution steps

Find the slope of

y = \frac{2 x}{x + 5} : \frac{d y}{d x} = \frac{10}{( x + 5 ) ^{2}}

Compute the slope of

y = \frac{2 x}{x + 5}

(5, 1) : m = \frac{1}{10}

Find the line with slope m=

\frac{1}{10}

and passing through

(5, 1) : y = \frac{1}{10} x + \frac{1}{2}

y = \frac{1}{10} x + \frac{1}{2}

\frac{d ^{2}}{d x ^{2}} (3 x^{2} - 5 y^{2})

\frac{d}{d x} (1 + 6 x)

x - 2

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

\frac{2}{ln ( x )}

What is the tangent of y=(2x)/(x+5),(5,1) ?
The tangent of y=(2x)/(x+5),(5,1) is y= 1/10 x+1/2