Differentiate the following functions with respect to x:
Let, y =
We have to find dy/dx
As we can observe that y is a fraction of two functions say u and v where,
u = sin x – x cos x and v = x sin x + cos x
∴ y = u/v
As we know that to find the derivative of fraction of two function we apply quotient rule of differentiation.
By quotient rule, we have –
…equation 1
u = – (x cos x – sin x)
Using algebra of derivatives –
⇒
∵
∴ {using product rule}
⇒ …equation 2
As, v = x sin x + cos x
∴
Using algebra of derivatives –
⇒
∵
∴ {using product rule}
⇒ …equation 3
∴ from equation 1, we can find dy/dx
∴
using equation 2 and 3, we get –
⇒
⇒
⇒
Hence,