Differentiate the following with respect to x :

Let, y =

⇒ y =

We have to find dy/dx.

Let, tan θ = 6^x

Differentiating both sides w.r.t x and using chain rule-

⇒

⇒ …(1) [∵ sec² θ = 1 + tan²θ ]

Similarly,

y =

we know that- sin2θ =

∴ y = sin^-1(sin 2θ ) = 2θ [using ITF basic properties]

∴

Using equation 1 we get –