What is the tangent of 2/(3x+5) ?

The tangent of 2/(3x+5) is y=-6/((3a_{0)+5)^2}x+(12a_{0}+10)/((3a_{0)+5)^2}

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tangent of 2/(3x+5)

tangent of

\frac{2}{3 x + 5}

y = - \frac{6}{( 3 a _{0} + 5 ) ^{2}} x + \frac{12 a _{0} + 10}{( 3 a _{0} + 5 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{3 a _{0} + 5})

Find the slope of

y = \frac{2}{3 x + 5} : \frac{d y}{d x} = - \frac{6}{( 3 x + 5 ) ^{2}}

Compute the slope of

y = \frac{2}{3 x + 5}

x = a_{0} : m = - \frac{6}{( 3 a _{0} + 5 ) ^{2}}

Find the line with slope m=

- \frac{6}{( 3 a _{0} + 5 ) ^{2}}

and passing through

(a_{0}, \frac{2}{3 a _{0} + 5}) : y = - \frac{6}{( 3 a _{0} + 5 ) ^{2}} x + \frac{12 a _{0} + 10}{( 3 a _{0} + 5 ) ^{2}}

y = - \frac{6}{( 3 a _{0} + 5 ) ^{2}} x + \frac{12 a _{0} + 10}{( 3 a _{0} + 5 ) ^{2}}

\int \frac{cot ( x )}{ln ( sin ( x ) )} d x

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

\int_{0}^{1} 2 x e^{- x^{2}} d x

\frac{d}{d x} (4 x^{4} + 2 x^{3} - x + 1)

What is the tangent of 2/(3x+5) ?
The tangent of 2/(3x+5) is y=-6/((3a_{0)+5)^2}x+(12a_{0}+10)/((3a_{0)+5)^2}