What is the tangent of 6/(x+4) ?

The tangent of 6/(x+4) is y=-6/((a_{0)+4)^2}x+(12a_{0}+24)/((a_{0)+4)^2}

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tangent of 6/(x+4)

tangent of

\frac{6}{x + 4}

y = - \frac{6}{( a _{0} + 4 ) ^{2}} x + \frac{12 a _{0} + 24}{( a _{0} + 4 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{6}{a _{0} + 4})

Find the slope of

y = \frac{6}{x + 4} : \frac{d y}{d x} = - \frac{6}{( x + 4 ) ^{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{6}{( a _{0} + 4 ) ^{2}}

Find the line with slope m=

- \frac{6}{( a _{0} + 4 ) ^{2}}

and passing through

(a_{0}, \frac{6}{a _{0} + 4}) : y = - \frac{6}{( a _{0} + 4 ) ^{2}} x + \frac{12 a _{0} + 24}{( a _{0} + 4 ) ^{2}}

y = - \frac{6}{( a _{0} + 4 ) ^{2}} x + \frac{12 a _{0} + 24}{( a _{0} + 4 ) ^{2}}

x \to - 2 - lim (ln (x + 3))

\frac{2}{\frac{1}{4} + h} - 4

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

y = x^{4} e^{- x}, (1, \frac{1}{e})

\int \frac{1}{( 100 - x ^{2} ) ^{2}} d x

What is the tangent of 6/(x+4) ?
The tangent of 6/(x+4) is y=-6/((a_{0)+4)^2}x+(12a_{0}+24)/((a_{0)+4)^2}