What is the tangent of y=(x^2)/(x+5),(1, 1/6) ?

The tangent of y=(x^2)/(x+5),(1, 1/6) is y= 11/36 x-5/36

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tangent of y=(x^2)/(x+5),(1, 1/6)

tangent of

y = \frac{x ^{2}}{x + 5}, (1, \frac{1}{6})

y = \frac{11}{36} x - \frac{5}{36}

Solution steps

Find the slope of

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

Compute the slope of

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

(1, \frac{1}{6}) : m = \frac{11}{36}

Find the line with slope m=

\frac{11}{36}

and passing through

(1, \frac{1}{6}) : y = \frac{11}{36} x - \frac{5}{36}

y = \frac{11}{36} x - \frac{5}{36}

\frac{\partial}{\partial x} (\frac{1}{x} + \frac{1}{y + z})

\frac{\partial}{\partial x} (y x^{2} z^{2} - x y^{4} + x z)

\frac{d}{d x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

f (x) = lo g_{41} (2 x - 4)

\frac{d}{d x} (ln (x) cos (x))

What is the tangent of y=(x^2)/(x+5),(1, 1/6) ?
The tangent of y=(x^2)/(x+5),(1, 1/6) is y= 11/36 x-5/36