Question

differentiate the following function with respect to X
1) (tan x)^sinx​

Answer 1

Answer:

tan x)^(-sinx)/(secx + log (cosx)

Step-by-step explanation:

y = (tan x)^sinx

log y = sinx log tanx

d/dx(log y) = d/dx(sinx log tanx)

= 1/y dx/dy = sinx(1/tanx)(sec^2x) + logx(cosx)

1/y dx/dy = cosx sec^2x + log (cosx)

1/y dx/dy = secx + log (cosx)

dx/dy = [secx + log (cosx)] y

dy/dx = 1/[secx + log (cosx)] y

dy/dx = (tan x)^(-sinx)/(secx + log (cosx)