Question

If y= e^1/2log (1+tan^2x) then find dy/dx. note- from 1/2 till x is in the upper limit.

Answer 1

Answer:

⇒ddx(elog(1+tan2(x)√))

=ddx(elog(sec(x))) (simplification using trig identities)

Now, use the triple composition rule for derivatives - the outermost function is ex, then it’s log(x), and the innermost function is sec(x):

=elog(sec(x))⋅1sec(x)ln(10)⋅sec(x)tan(x)

Combine terms together:

=elog(sec(x))sec(x)tan(x)sec(x)ln(10)

Simplify it:

=tan(x)elog(sec(x))ln(10)

I hope this helps!

Step-by-step explanation: