Differentiate with respect to x xn loga x

Let us consider y = xⁿ log_a 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 = log_a x

y = uv

Now let us apply product rule of differentiation.

By using product rule, we get

\( \dfrac{dy}{dx}=x^{n-1}(nlog_ax+\dfrac{1}{log a})\)