What is the tangent of-6/((3x+5)^2) ?

The tangent of-6/((3x+5)^2) is y=(36)/((3a_{0)+5)^3}x+(-54a_{0}-30)/((3a_{0)+5)^3}

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tangent of-6/((3x+5)^2)

tangent of

- \frac{6}{( 3 x + 5 ) ^{2}}

y = \frac{36}{( 3 a _{0} + 5 ) ^{3}} x + \frac{- 54 a _{0} - 30}{( 3 a _{0} + 5 ) ^{3}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = - \frac{6}{( 3 x + 5 ) ^{2}} : \frac{d y}{d x} = \frac{36}{( 3 x + 5 ) ^{3}}

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{36}{( 3 a _{0} + 5 ) ^{3}}

Find the line with slope m=

\frac{36}{( 3 a _{0} + 5 ) ^{3}}

and passing through

(a_{0}, - \frac{6}{( 3 a _{0} + 5 ) ^{2}}) : y = \frac{36}{( 3 a _{0} + 5 ) ^{3}} x + \frac{- 54 a _{0} - 30}{( 3 a _{0} + 5 ) ^{3}}

y = \frac{36}{( 3 a _{0} + 5 ) ^{3}} x + \frac{- 54 a _{0} - 30}{( 3 a _{0} + 5 ) ^{3}}

\int_{3}^{\infty} e^{7 x} d x

\frac{\partial}{\partial x} (3 x (5 + y)^{- 1})

\frac{d y}{d x} + y = 1, y (0) = 1

\frac{\partial}{\partial y} ((y - x^{2})^{2} + x^{5})

\frac{d}{d x} (22 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

What is the tangent of-6/((3x+5)^2) ?
The tangent of-6/((3x+5)^2) is y=(36)/((3a_{0)+5)^3}x+(-54a_{0}-30)/((3a_{0)+5)^3}