# Slope of the curve

#### muhammetbalikci

Question: Find the slope of the curve's graph at the given point. Then find the equation of tangent and normal line to be graph if exist. I need to your help.

y = 2tan(pi.x/4) at x=1

#### Idea

$$\displaystyle f(x)= 2 \tan \left(\frac{\pi x}{4}\right)$$

$$\displaystyle f(1)=2$$

The equation of the tangent line is of the form

$$\displaystyle y-2=m(x-1)$$

#### muhammetbalikci

Thank you very much. But how can we calculate the derivative of this equation? I couldn't do it.

#### Cervesa

chain rule

$y' = 2\sec^2\left(\dfrac{\pi x}{4}\right) \cdot \dfrac{\pi}{4}$