Question

find an equation of the tangent line to the curve y=9tanx at the point (π/4, 9)

Answer 1

The tangent line to $y(x)$ at $x=\dfrac\pi4$ has slope $y'\left(\dfrac\pi4\right)$, so first we compute the derivative:

$y'(x)=9\sec^2x$

and evaluate it at the point of interest to find the slope:

$y'\left(\dfrac\pi4\right)=9\sec^2\dfrac\pi4=18$

Then the equation of the tangent line is

$y-9=18\left(x-\dfrac\pi4\right)\implies y=18x+9-\dfrac{9\pi}2$