What is the tangent of 6/(5x+3) ?

The tangent of 6/(5x+3) is y=-(30)/((5a_{0)+3)^2}x+(60a_{0}+18)/((5a_{0)+3)^2}

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tangent of 6/(5x+3)

tangent of

\frac{6}{5 x + 3}

y = - \frac{30}{( 5 a _{0} + 3 ) ^{2}} x + \frac{60 a _{0} + 18}{( 5 a _{0} + 3 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{6}{5 a _{0} + 3})

Find the slope of

y = \frac{6}{5 x + 3} : \frac{d y}{d x} = - \frac{30}{( 5 x + 3 ) ^{2}}

Compute the slope of

y = \frac{6}{5 x + 3}

x = a_{0} : m = - \frac{30}{( 5 a _{0} + 3 ) ^{2}}

Find the line with slope m=

- \frac{30}{( 5 a _{0} + 3 ) ^{2}}

and passing through

(a_{0}, \frac{6}{5 a _{0} + 3}) : y = - \frac{30}{( 5 a _{0} + 3 ) ^{2}} x + \frac{60 a _{0} + 18}{( 5 a _{0} + 3 ) ^{2}}

y = - \frac{30}{( 5 a _{0} + 3 ) ^{2}} x + \frac{60 a _{0} + 18}{( 5 a _{0} + 3 ) ^{2}}

u (x) = 2 x

\frac{d}{d x} (cos (e^{3 x}) - sin (e^{3 x}))

\int 5 sin (x) ln (sin (x)) d x

n = 0 \sum \infty n^{0.5}

\int (\frac{x}{x}) d x

What is the tangent of 6/(5x+3) ?
The tangent of 6/(5x+3) is y=-(30)/((5a_{0)+3)^2}x+(60a_{0}+18)/((5a_{0)+3)^2}