What is the tangent of f(x)=arctan(x/2),\at x=2 ?

The tangent of f(x)=arctan(x/2),\at x=2 is y= 1/4 x+pi/4-1/2

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tangent of f(x)=arctan(x/2),\at x=2

tangent of

f (x) = arctan (\frac{x}{2}), at x = 2

y = \frac{1}{4} x + \frac{π}{4} - \frac{1}{2}

Solution steps

Find the tangent point:

(2, \frac{π}{4})

Find the slope of

f (x) = arctan (\frac{x}{2}) : \frac{df ( x )}{d x} = \frac{2}{x ^{2} + 4}

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{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(2, \frac{π}{4}) : y = \frac{1}{4} x + \frac{π}{4} - \frac{1}{2}

y = \frac{1}{4} x + \frac{π}{4} - \frac{1}{2}

2 x + 6, - 2, 2

y = ln (x^{2} - 2 x + 1), (2, 0)

\frac{d}{d x} (2^{s i n (x)})

\int_{0}^{4} \frac{ln ( x )}{x} d x

sin^{2} (x)

What is the tangent of f(x)=arctan(x/2),\at x=2 ?
The tangent of f(x)=arctan(x/2),\at x=2 is y= 1/4 x+pi/4-1/2