Differentiate the following functions with respect to x:
(ax + b)n(cx + d)m
Let, y = (ax + b)n(cx + d)m
We have to find dy/dx
As we can observe that y is a product of two functions say u and v where,
u = (ax + b)n and v = (cx + d)m
∴ 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 = (ax + b)n
As,
∴ …equation 2
As, v = (cx + d)m
As,
…equation 3
∴ from equation 1, we can find dy/dx
∴
{using equation 2 & 3}
⇒
⇒
Hence,