Math Is Fun Forum

666 bro

Member

From: Flatland

Registered: 2019-04-26

Posts: 706

Difference between sin^n(x) and sin(x^n)

How sin^n(x) is different from sin(x^n) while differentiating them?

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"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Difference between sin^n(x) and sin(x^n)

hi 666 bro

If you say "sin x to the power n" some people might not be clear if you mean find sin(x) and raise that to the power n or raise x to the power n and then find the sine of that .

This arises because, in English maths, where to put the function in an expression is inconsistent.  Sometimes the function comes after the input such as x^2 and sometimes the function comes first such as √x.

If

To differentiate use the chain rule;

If

This time the chain rule gives

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

666 bro

Member

From: Flatland

Registered: 2019-04-26

Posts: 706

Re: Difference between sin^n(x) and sin(x^n)

Thanks a lot

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"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan