What is the tangent of (23)/((8x-1)^2) ?

The tangent of (23)/((8x-1)^2) is y=-(368)/((8a_{0)-1)^3}x+(552a_{0}-23)/((8a_{0)-1)^3}

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tangent of (23)/((8x-1)^2)

tangent of

\frac{23}{( 8 x - 1 ) ^{2}}

y = - \frac{368}{( 8 a _{0} - 1 ) ^{3}} x + \frac{552 a _{0} - 23}{( 8 a _{0} - 1 ) ^{3}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{23}{( 8 a _{0} - 1 ) ^{2}})

Find the slope of

y = \frac{23}{( 8 x - 1 ) ^{2}} : \frac{d y}{d x} = - \frac{368}{( 8 x - 1 ) ^{3}}

Compute the slope of

y = \frac{23}{( 8 x - 1 ) ^{2}}

x = a_{0} : m = - \frac{368}{( 8 a _{0} - 1 ) ^{3}}

Find the line with slope m=

- \frac{368}{( 8 a _{0} - 1 ) ^{3}}

and passing through

(a_{0}, \frac{23}{( 8 a _{0} - 1 ) ^{2}}) : y = - \frac{368}{( 8 a _{0} - 1 ) ^{3}} x + \frac{552 a _{0} - 23}{( 8 a _{0} - 1 ) ^{3}}

y = - \frac{368}{( 8 a _{0} - 1 ) ^{3}} x + \frac{552 a _{0} - 23}{( 8 a _{0} - 1 ) ^{3}}

x^{7}

\int \frac{cos ( 3 x )}{sin ^{2} ( 3 x )} d x

x e^{x}, 1 \leq x \leq 7

\frac{\partial}{\partial x} (x^{2} y^{\frac{1}{3}})

What is the tangent of (23)/((8x-1)^2) ?
The tangent of (23)/((8x-1)^2) is y=-(368)/((8a_{0)-1)^3}x+(552a_{0}-23)/((8a_{0)-1)^3}