Differentiate with respect to x xn tan x

Let us consider y = xⁿ tan x

We need to find \( \dfrac{dy}{dx}\)

We know that y is a product of two functions say u and v where,

u = xⁿ and v = tan x

y = uv

Now let us apply product rule of differentiation.

By using product rule, we get

\( \dfrac{dy}{dx}=x^{n-1}(ntanx+x sec^2x)\)