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=\frac\pi4` has slope
`y'\left(\frac\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(\frac\pi4\right)=9\sec^2\frac\pi4=18`

Then the equation of the tangent line is

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