What is the tangent of 4/(x+2) ?

The tangent of 4/(x+2) is y=-4/((a_{0)+2)^2}x+(8a_{0}+8)/((a_{0)+2)^2}

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tangent of 4/(x+2)

tangent of

\frac{4}{x + 2}

y = - \frac{4}{( a _{0} + 2 ) ^{2}} x + \frac{8 a _{0} + 8}{( a _{0} + 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{4}{a _{0} + 2})

Find the slope of

y = \frac{4}{x + 2} : \frac{d y}{d x} = - \frac{4}{( x + 2 ) ^{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{4}{( a _{0} + 2 ) ^{2}}

Find the line with slope m=

- \frac{4}{( a _{0} + 2 ) ^{2}}

and passing through

(a_{0}, \frac{4}{a _{0} + 2}) : y = - \frac{4}{( a _{0} + 2 ) ^{2}} x + \frac{8 a _{0} + 8}{( a _{0} + 2 ) ^{2}}

y = - \frac{4}{( a _{0} + 2 ) ^{2}} x + \frac{8 a _{0} + 8}{( a _{0} + 2 ) ^{2}}

\int \frac{4 t ^{3} - 3 t ^{2} + 4 t}{t ^{2} + 1} d t

\int \frac{4 x}{( x ^{2} + 4 ) ^{2}} d x

\frac{\partial}{\partial x} (x e^{y} + y e^{x})

\int_{0}^{1} \frac{49}{x ^{5}} d x

7 x, at x = 4

What is the tangent of 4/(x+2) ?
The tangent of 4/(x+2) is y=-4/((a_{0)+2)^2}x+(8a_{0}+8)/((a_{0)+2)^2}