What is the tangent of 1/(3+2x) ?

The tangent of 1/(3+2x) is y=-2/((3+2a_{0))^2}x+(4a_{0}+3)/((2a_{0)+3)^2}

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tangent of 1/(3+2x)

tangent of

\frac{1}{3 + 2 x}

y = - \frac{2}{( 3 + 2 a _{0} ) ^{2}} x + \frac{4 a _{0} + 3}{( 2 a _{0} + 3 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{3 + 2 a _{0}})

Find the slope of

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

Compute the slope of

y = \frac{1}{3 + 2 x}

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

Find the line with slope m=

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

and passing through

(a_{0}, \frac{1}{3 + 2 a _{0}}) : y = - \frac{2}{( 3 + 2 a _{0} ) ^{2}} x + \frac{4 a _{0} + 3}{( 2 a _{0} + 3 ) ^{2}}

y = - \frac{2}{( 3 + 2 a _{0} ) ^{2}} x + \frac{4 a _{0} + 3}{( 2 a _{0} + 3 ) ^{2}}

\frac{1}{1 - x}, 0

x \to 0 + lim (ln^{2} (x))

x \to 2 lim (\frac{x + 6}{x ^{2}})

x \to 0.9 lim (x^{2} + 3 x + 2)

\frac{\partial}{\partial x} (- ak sin (k x - wt))

What is the tangent of 1/(3+2x) ?
The tangent of 1/(3+2x) is y=-2/((3+2a_{0))^2}x+(4a_{0}+3)/((2a_{0)+3)^2}