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 = ex – tan x and v = cot x – xn
∴ 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
As, u = ex – tan x
∴
∵ , so we get –
⇒ …equation 2
As, v = cot x – xn
∵ , so we get –
⇒ …equation 3
∴ from equation 1, we can find dy/dx
∴
using equation 2 and 3, we get –
⇒
⇒
Hence,