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

The tangent of (-5x^2)/(2x+3) is y=-(5(2a_{0}^2+6a_{0}))/((2a_{0)+3)^2}x+(15a_{0}^2)/((2a_{0)+3)^2}

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tangent of (-5x^2)/(2x+3)

tangent of

\frac{- 5 x ^{2}}{2 x + 3}

y = - \frac{5 ( 2 a _{0}^{2} + 6 a _{0} )}{( 2 a _{0} + 3 ) ^{2}} x + \frac{15 a _{0}^{2}}{( 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{5 a _{0}^{2}}{2 a _{0} + 3})

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{5 ( 2 a _{0}^{2} + 6 a _{0} )}{( 2 a _{0} + 3 ) ^{2}}

Find the line with slope m=

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

and passing through

(a_{0}, - \frac{5 a _{0}^{2}}{2 a _{0} + 3}) : y = - \frac{5 ( 2 a _{0}^{2} + 6 a _{0} )}{( 2 a _{0} + 3 ) ^{2}} x + \frac{15 a _{0}^{2}}{( 2 a _{0} + 3 ) ^{2}}

y = - \frac{5 ( 2 a _{0}^{2} + 6 a _{0} )}{( 2 a _{0} + 3 ) ^{2}} x + \frac{15 a _{0}^{2}}{( 2 a _{0} + 3 ) ^{2}}

What is the tangent of (-5x^2)/(2x+3) ?
The tangent of (-5x^2)/(2x+3) is y=-(5(2a_{0}^2+6a_{0}))/((2a_{0)+3)^2}x+(15a_{0}^2)/((2a_{0)+3)^2}