What is the tangent of f(x)=(e^x)/(x+6),(0, 1/6) ?

The tangent of f(x)=(e^x)/(x+6),(0, 1/6) is y= 5/36 x+1/6

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tangent of f(x)=(e^x)/(x+6),(0, 1/6)

tangent of

f (x) = \frac{e ^{x}}{x + 6}, (0, \frac{1}{6})

y = \frac{5}{36} x + \frac{1}{6}

Solution steps

Find the slope of

f (x) = \frac{e ^{x}}{x + 6} : \frac{df ( x )}{d x} = \frac{e ^{x} x + 5 e ^{x}}{( x + 6 ) ^{2}}

Compute the slope of

f (x) = \frac{e ^{x}}{x + 6}

(0, \frac{1}{6}) : m = \frac{5}{36}

Find the line with slope m=

\frac{5}{36}

and passing through

(0, \frac{1}{6}) : y = \frac{5}{36} x + \frac{1}{6}

y = \frac{5}{36} x + \frac{1}{6}

f (x) = (x + 2 x) e^{x}

\int \frac{13}{13 + e ^{x}} d x

\frac{d y}{d x} = 6 - 3 x^{2}

\int e^{x} \cdot x^{- 1} d x

\frac{d y}{d x} = \frac{4 y ln ( x )}{x}

What is the tangent of f(x)=(e^x)/(x+6),(0, 1/6) ?
The tangent of f(x)=(e^x)/(x+6),(0, 1/6) is y= 5/36 x+1/6