What is the tangent of f(x)=5cot(x),\at x= pi/4 ?

The tangent of f(x)=5cot(x),\at x= pi/4 is y=-10x+5+(5pi)/2

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tangent of f(x)=5cot(x),\at x= pi/4

tangent of

f (x) = 5 cot (x), at x = \frac{π}{4}

y = - 10 x + 5 + \frac{5 π}{2}

Solution steps

Find the tangent point:

(\frac{π}{4}, 5)

Find the slope of

f (x) = 5 cot (x) : \frac{df ( x )}{d x} = - 5 csc^{2} (x)

Compute the slope of

f (x) = 5 cot (x)

x = \frac{π}{4} : m = - 10

Find the line with slope m=

- 10

and passing through

(\frac{π}{4}, 5) : y = - 10 x + 5 + \frac{5 π}{2}

y = - 10 x + 5 + \frac{5 π}{2}

\frac{d y}{d x}, x + y = x^{2}

y^{^{''}} - 6 y^{^{'}} - 27 y = 0

\int \frac{1}{y - x} d y

\int (1. 8^{0.045 x} - 1) d x

f (x) = e^{\frac{x}{3}}

What is the tangent of f(x)=5cot(x),\at x= pi/4 ?
The tangent of f(x)=5cot(x),\at x= pi/4 is y=-10x+5+(5pi)/2