What is the tangent of y=((x+5)^5)/(7x-5) ?

The tangent of y=((x+5)^5)/(7x-5) is

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tangent of y=((x+5)^5)/(7x-5)

tangent of

y = \frac{( x + 5 ) ^{5}}{7 x - 5}

y = \frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}} x + \frac{- 21 a _{0}^{6} - 330 a _{0}^{5} - 1375 a _{0}^{4} + 2500 a _{0}^{3} + 28125 a _{0}^{2} + 43750 a _{0} - 15625}{( 7 a _{0} - 5 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{( a _{0} + 5 ) ^{5}}{7 a _{0} - 5})

Find the slope of

y = \frac{( x + 5 ) ^{5}}{7 x - 5} : \frac{d y}{d x} = \frac{5 ( x + 5 ) ^{4} ( 7 x - 5 ) - 7 ( x + 5 ) ^{5}}{( 7 x - 5 ) ^{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{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}}

Find the line with slope m=

\frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}}

and passing through

(a_{0}, \frac{( a _{0} + 5 ) ^{5}}{7 a _{0} - 5}) : y = \frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}} x + \frac{- 21 a _{0}^{6} - 330 a _{0}^{5} - 1375 a _{0}^{4} + 2500 a _{0}^{3} + 28125 a _{0}^{2} + 43750 a _{0} - 15625}{( 7 a _{0} - 5 ) ^{2}}

y = \frac{28 a _{0}^{5} + 500 a _{0}^{4} + 3000 a _{0}^{3} + 5000 a _{0}^{2} - 12500 a _{0} - 37500}{( 7 a _{0} - 5 ) ^{2}} x + \frac{- 21 a _{0}^{6} - 330 a _{0}^{5} - 1375 a _{0}^{4} + 2500 a _{0}^{3} + 28125 a _{0}^{2} + 43750 a _{0} - 15625}{( 7 a _{0} - 5 ) ^{2}}

\int_{0}^{6} 2 π x (6 x - x^{2}) d x

\frac{d}{d x} (cos^{2} (x) - cos (x))

\frac{d}{d x} (m (m - 1) x^{m - 2})

\frac{d}{d x} (arctan (1))

\int (1 - x^{\frac{3}{2}})^{\frac{5}{3}} \cdot x d x

What is the tangent of y=((x+5)^5)/(7x-5) ?
The tangent of y=((x+5)^5)/(7x-5) is