What is the tangent of (4x)/(x+3) ?

The tangent of (4x)/(x+3) is y=(12)/((a_{0)+3)^2}x+(4a_{0}^2)/((a_{0)+3)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of (4x)/(x+3)

tangent of

\frac{4 x}{x + 3}

y = \frac{12}{( a _{0} + 3 ) ^{2}} x + \frac{4 a _{0}^{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{4 a _{0}}{a _{0} + 3})

Find the slope of

y = \frac{4 x}{x + 3} : \frac{d y}{d x} = \frac{12}{( x + 3 ) ^{2}}

Compute the slope of

y = \frac{4 x}{x + 3}

x = a_{0} : m = \frac{12}{( a _{0} + 3 ) ^{2}}

Find the line with slope m=

\frac{12}{( a _{0} + 3 ) ^{2}}

and passing through

(a_{0}, \frac{4 a _{0}}{a _{0} + 3}) : y = \frac{12}{( a _{0} + 3 ) ^{2}} x + \frac{4 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

y = \frac{12}{( a _{0} + 3 ) ^{2}} x + \frac{4 a _{0}^{2}}{( a _{0} + 3 ) ^{2}}

y = \frac{2}{x}

\frac{\partial}{\partial x} (3 x^{4} e^{x^{2} y})

x \to - 3 + lim (\frac{3}{x ^{2} - 9})

x \frac{d y}{d x} + 22 y = \frac{1}{x}

\frac{e ^{2 x} - e ^{x} + 1}{e ^{x}}

What is the tangent of (4x)/(x+3) ?
The tangent of (4x)/(x+3) is y=(12)/((a_{0)+3)^2}x+(4a_{0}^2)/((a_{0)+3)^2}