Q. 53.5( 2 Votes )
Differentiate the following functions with respect to x:
xn loga x
Answer :
Let, y = xn log a x
We have to find dy/dx
As we can observe that y is a product of two functions say u and v where,
u = xn and v = log a x
∴ y = uv
As we know that to find the derivative of product of two function we apply product rule of differentiation.
By product rule, we have –
…equation 1
As, u = xn
∴ 
…equation 2 {∵ 
}
As, v = loga x
…equation 3 {∵ 
}
∴ from equation 1, we can find dy/dx
∴ 
⇒ 
{using equation 2 & 3}
Hence,
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