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

The tangent of y=(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 y=(2x+3)/(3x-2)

tangent of

y = \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

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

Compute the slope of

y = \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 9 cos (x) + 5 d x

\frac{\partial}{\partial x} (x^{0.1} y^{0.9})

x \to 0 lim (\frac{sin ( 4 x ^{2} )}{x})

\frac{\partial}{\partial x} (x \cdot y^{2} \cdot z^{3})

(4 x - 3)^{5} (3 - x^{3})^{2}

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