What is the tangent of (5x-3)^4(2x-7)^{-3} ?

The tangent of (5x-3)^4(2x-7)^{-3} is

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tangent of (5x-3)^4(2x-7)^{-3}

tangent of

(5 x - 3)^{4} (2 x - 7)^{- 3}

y = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}} x + \frac{10125 a _{0}^{4} - 15600 a _{0}^{3} + 6210 a _{0}^{2} + 648 a _{0} - 567}{( 2 a _{0} - 7 ) ^{4}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{( 5 a _{0} - 3 ) ^{4}}{( 2 a _{0} - 7 ) ^{3}})

Find the slope of

y = (5 x - 3)^{4} (2 x - 7)^{- 3} : \frac{d y}{d x} = \frac{20 ( 5 x - 3 ) ^{3}}{( 2 x - 7 ) ^{3}} - \frac{6 ( 5 x - 3 ) ^{4}}{( 2 x - 7 ) ^{4}}

Compute the slope of

y = (5 x - 3)^{4} (2 x - 7)^{- 3}

x = a_{0} : m = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}}

Find the line with slope m=

\frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}}

and passing through

(a_{0}, \frac{( 5 a _{0} - 3 ) ^{4}}{( 2 a _{0} - 7 ) ^{3}}) : y = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}} x + \frac{10125 a _{0}^{4} - 15600 a _{0}^{3} + 6210 a _{0}^{2} + 648 a _{0} - 567}{( 2 a _{0} - 7 ) ^{4}}

y = \frac{1250 a _{0}^{4} - 17500 a _{0}^{3} + 28800 a _{0}^{2} - 16740 a _{0} + 3294}{( 2 a _{0} - 7 ) ^{4}} x + \frac{10125 a _{0}^{4} - 15600 a _{0}^{3} + 6210 a _{0}^{2} + 648 a _{0} - 567}{( 2 a _{0} - 7 ) ^{4}}

\frac{\partial}{\partial y} (0.2 y - 7)

0.35 (sin (x))

\frac{\partial}{\partial r} (2 rs)

\int cos (\frac{1}{2}) y d y

\frac{d}{d x} (\frac{x + ln ( x )}{x})

What is the tangent of (5x-3)^4(2x-7)^{-3} ?
The tangent of (5x-3)^4(2x-7)^{-3} is