What is the tangent of 4cot^7(x),\at x= pi/4 ?

The tangent of 4cot^7(x),\at x= pi/4 is y=-56x+4+14pi

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tangent of 4cot^7(x),\at x= pi/4

tangent of

4 cot^{7} (x), at x = \frac{π}{4}

y = - 56 x + 4 + 14 π

Solution steps

Find the tangent point:

(\frac{π}{4}, 4)

Find the slope of

y = 4 cot^{7} (x) : \frac{d y}{d x} = - 28 cot^{6} (x) csc^{2} (x)

Compute the slope of

y = 4 cot^{7} (x)

x = \frac{π}{4} : m = - 56

Find the line with slope m=

- 56

and passing through

(\frac{π}{4}, 4) : y = - 56 x + 4 + 14 π

y = - 56 x + 4 + 14 π

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

x \to 8 lim (\frac{3 x ^{2} - 24 x}{x ^{2} - 64})

x \to 2 lim (\frac{( x + 1 )}{x - 2})

\frac{d}{d x} (2 x - sin (2 x))

\frac{d}{d x} (x^{3} - 3 x + 3)

What is the tangent of 4cot^7(x),\at x= pi/4 ?
The tangent of 4cot^7(x),\at x= pi/4 is y=-56x+4+14pi