What is the tangent of y=arctan(-x),\at x=4 ?

The tangent of y=arctan(-x),\at x=4 is y=-1/17 x-arctan(4)+4/17

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tangent of y=arctan(-x),\at x=4

tangent of

y = arctan (- x), at x = 4

y = - \frac{1}{17} x - arctan (4) + \frac{4}{17}

Solution steps

Find the tangent point:

(4, - arctan (4))

Find the slope of

y = arctan (- x) : \frac{d y}{d x} = - \frac{1}{x ^{2} + 1}

Compute the slope of

y = arctan (- x)

x = 4 : m = - \frac{1}{17}

Find the line with slope m=

- \frac{1}{17}

and passing through

(4, - arctan (4)) : y = - \frac{1}{17} x - arctan (4) + \frac{4}{17}

y = - \frac{1}{17} x - arctan (4) + \frac{4}{17}

\frac{d}{d x} (\frac{1}{2} x - \frac{1}{3})

y = x^{4} e^{2 x}

\frac{d}{d x} (x^{3} - 6 x^{2} - 9)

x \to 0 + lim (\frac{4}{x} - \frac{4}{∣ x ∣})

t \to 0 lim (t e^{- t})

What is the tangent of y=arctan(-x),\at x=4 ?
The tangent of y=arctan(-x),\at x=4 is y=-1/17 x-arctan(4)+4/17