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A day full of math games & activities. Find one near you.
Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (ax + b)ⁿ
Solution:
The given function is f(x) = (ax + b)ⁿ. It can be written as f(x) = (ax + b) (ax + b) (ax + b) ... (ax + b) (n times).
Using the product rule, its derivative is,
d/dx (f(x)) = [ (ax + b) (ax + b) ... (ax + b) (n-1) times d/dx (ax + b)
+ (ax + b) (ax + b) ... (ax + b) (n-1) times d/dx (ax + b)
+ ... + (ax + b) (ax + b) ... (ax + b) (n-1) times d/dx (ax + b) ] (n times)
= (ax + b) (ax + b) ... (ax + b) (n-1) times [ a + a + ... + a (n times)]
= (ax + b)n-1 [na]
= na (ax + b)n-1
NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 12
Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (ax + b)ⁿ
Summary:
The derivative of the given function (ax + b)ⁿ is na (ax + b)n-1
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