What is the tangent of 3/(x+1) ?

The tangent of 3/(x+1) is y=-3/((a_{0)+1)^2}x+(6a_{0}+3)/((a_{0)+1)^2}

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tangent of 3/(x+1)

tangent of

\frac{3}{x + 1}

y = - \frac{3}{( a _{0} + 1 ) ^{2}} x + \frac{6 a _{0} + 3}{( a _{0} + 1 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{3}{a _{0} + 1})

Find the slope of

y = \frac{3}{x + 1} : \frac{d y}{d x} = - \frac{3}{( x + 1 ) ^{2}}

Compute the slope of

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

x = a_{0} : m = - \frac{3}{( a _{0} + 1 ) ^{2}}

Find the line with slope m=

- \frac{3}{( a _{0} + 1 ) ^{2}}

and passing through

(a_{0}, \frac{3}{a _{0} + 1}) : y = - \frac{3}{( a _{0} + 1 ) ^{2}} x + \frac{6 a _{0} + 3}{( a _{0} + 1 ) ^{2}}

y = - \frac{3}{( a _{0} + 1 ) ^{2}} x + \frac{6 a _{0} + 3}{( a _{0} + 1 ) ^{2}}

\int (5^{x} + 2^{5}) d x

f (x) = 8 x e^{x} - 8 e^{x}

y = 3 x + 1, (8, 5)

\frac{d}{d x} (\frac{x ^{4}}{e ^{x}})

\frac{d}{d x} (x 4^{x})

What is the tangent of 3/(x+1) ?
The tangent of 3/(x+1) is y=-3/((a_{0)+1)^2}x+(6a_{0}+3)/((a_{0)+1)^2}