Differentiate the following functions with respect to x:
(x sin x + cos x)(ex + x2 log x)
Let, y = (x sin x + cos x)( ex + x2 log 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 = x sin x + cos x and v = (ex + x2 log 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 = x sin x + cos x
∴
Using algebra of derivatives –
⇒
∵
∴ {using product rule}
⇒ …equation 2
As, v = ex + x2 log x
Using algebra of derivatives –
⇒
∵
∴ {using product rule}
⇒ …equation 3
∴ from equation 1, we can find dy/dx
∴
using equation 2 & 3, we get –
⇒
⇒
Hence,