find the equation of the tangent line to the graph of the function at the given point
y=arctan 2/x, (2, pi/4)

Question

find the equation of the tangent line to the graph of the function at the given point
 y=arctan 2/x, (2, pi/4)

anonymous · Answer

well just differentiate it then find the gradient m since the x value is given 

then y -y_1 = m(x-x_1) i.e eqn. of tangent line

anonymous · Answer

$$f(x)=\arctan(\frac{2}{x})$$
$$f'(x)=\frac{-2}{x^2+4}$$
$$f'(2)=-\frac{1}{4}$$ then point - slope

amistre64 · Answer

or... :)$$tan(y)=\frac{2}{x}$$
$$sec^2(y)y'=-\frac{2}{x^2}$$
$$y'=-\frac{2cos^2(y)}{x^2}$$

amistre64 · Answer

$$y'=-\frac{2~cos^2(45^o)}{4}$$
$$y'=-\frac{cos^2(45^o)}{2}$$
$$y'=-\frac{1}{(\sqrt{2})^22}$$
$$y'=-\frac{1}{4}$$

lol