Q26 of 168 Page 30

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,



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