What is the tangent of f(x)=(2x+3)/(3x-2) ?

The tangent of f(x)=(2x+3)/(3x-2) is y=-(13)/((3a_{0)-2)^2}x+(6a_{0}^2+18a_{0}-6)/((3a_{0)-2)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of f(x)=(2x+3)/(3x-2)

tangent of

f (x) = \frac{2 x + 3}{3 x - 2}

y = - \frac{13}{( 3 a _{0} - 2 ) ^{2}} x + \frac{6 a _{0}^{2} + 18 a _{0} - 6}{( 3 a _{0} - 2 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = \frac{2 x + 3}{3 x - 2} : \frac{df ( x )}{d x} = - \frac{13}{( 3 x - 2 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x + 3}{3 x - 2}

x = a_{0} : m = - \frac{13}{( 3 a _{0} - 2 ) ^{2}}

Find the line with slope m=

- \frac{13}{( 3 a _{0} - 2 ) ^{2}}

and passing through

(a_{0}, \frac{2 a _{0} + 3}{3 a _{0} - 2}) : y = - \frac{13}{( 3 a _{0} - 2 ) ^{2}} x + \frac{6 a _{0}^{2} + 18 a _{0} - 6}{( 3 a _{0} - 2 ) ^{2}}

y = - \frac{13}{( 3 a _{0} - 2 ) ^{2}} x + \frac{6 a _{0}^{2} + 18 a _{0} - 6}{( 3 a _{0} - 2 ) ^{2}}

\int_{0}^{2} \frac{1}{8 + 2 x ^{2}} d x

3 ln (x), x ln (x), 1, 2

\frac{d y}{d x} = - \frac{e ^{x}}{8}

\int sec^{2} (3 x) tan^{3} (3 x) d x

x \cdot 6^{x}

What is the tangent of f(x)=(2x+3)/(3x-2) ?
The tangent of f(x)=(2x+3)/(3x-2) is y=-(13)/((3a_{0)-2)^2}x+(6a_{0}^2+18a_{0}-6)/((3a_{0)-2)^2}