What is the tangent of f(x)= x/(x^2+49) ?

The tangent of f(x)= x/(x^2+49) is y=(-a_{0}^2+49)/((a_{0)^2+49)^2}x+(2a_{0}^3)/((a_{0)^2+49)^2}

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tangent of f(x)= x/(x^2+49)

tangent of

f (x) = \frac{x}{x ^{2} + 49}

y = \frac{- a _{0}^{2} + 49}{( a _{0}^{2} + 49 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 49 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 49})

Find the slope of

f (x) = \frac{x}{x ^{2} + 49} : \frac{df ( x )}{d x} = \frac{- x ^{2} + 49}{( x ^{2} + 49 ) ^{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{- a _{0}^{2} + 49}{( a _{0}^{2} + 49 ) ^{2}}

Find the line with slope m=

\frac{- a _{0}^{2} + 49}{( a _{0}^{2} + 49 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 49}) : y = \frac{- a _{0}^{2} + 49}{( a _{0}^{2} + 49 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 49 ) ^{2}}

y = \frac{- a _{0}^{2} + 49}{( a _{0}^{2} + 49 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 49 ) ^{2}}

\frac{d}{d x} (2 ln ∣ x - e^{x} ∣)

\frac{\partial}{\partial y} (- \frac{1}{ln ( 10 ) ( x - y )})

f (x) = \frac{8}{sin ( x ) + cos ( x )}

f (x) = x^{2} - 12, g (x) = x - 6, [23, 6]

\int_{0}^{1} x - x d x

What is the tangent of f(x)= x/(x^2+49) ?
The tangent of f(x)= x/(x^2+49) is y=(-a_{0}^2+49)/((a_{0)^2+49)^2}x+(2a_{0}^3)/((a_{0)^2+49)^2}