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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the derivative of the following function (where n is an integer): sinⁿx
Solution:
The given function is f(x) = sinnx.
It can be written as
f(x) = sin x sin x sin x ... sin x (n times).
Using the product rule, its derivative is,
d/dx (f(x)) = [ sin x sin x ... sin x (n-1) times d/dx (sin x)
+ sin x sin x ... sin x (n-1) times d/dx (sin x)
+ ... + sin x sin x ... sin x (n-1) times d/dx (sin x) ] (n times)
= sin x sin x ... sin x (n-1) times [ cos x + cos x + ... + cos x (n times)]
= sinn-1 x [n cos x]
= n sinn-1x cos x
NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 19
Find the derivative of the following function (where n is an integer): sinⁿx
Summary:
The derivative of the given function sinⁿx is n sinn-1x cos x
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