Question

How do you differentiate `y= 10^ (tan (pi)(theta)`?

Answer 1

`dy/(dθ) = 10^tan(πθ) (πln(tan(πθ))) /cos^2(πθ)`

Explanation:

Let `v = πθ` and `u = tanv`.
Using the chain rule, `dy/(dθ) = dy/(du) (du)/(dv) (dv)/(dθ)`

So now, `y = 10^u`, so:

`dy/(dθ) = 10^u lnu * 1/cos^2(v) * π`

`= 10^tan(πθ) (πln(tan(πθ))) /cos^2(πθ)`