Math Is Fun Forum

greendragon

Member

Registered: 2016-03-27

Posts: 1

Antiderivatives involving linear compositions

I'm supposed to take antiderivatives like this

Now initially, one might think the antiderivative is this

Because the derivative of cosine is negative sine. It follows that the derivative of -cosine is sine.

However, that expression was actually two functions.

and

So we have to use the chain rule to differentiate that.

Now the derivative of a linear equation is just the slope m. In this case, 4. So we're left with

This means that we're off by 4, so we have to multiply 1/4th to our previous guess. I thought we were supposed to end up with this

Instead the answer is

I don't understand why you have to reverse the sign here

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Antiderivatives involving linear compositions

hi greendragon

Your initial 'guess' was right.  The chain rule on that gives minus and 4 so you need an improved guess of

Your last line is not correct ... it should be cosine.

You said why you need the minus yourself. 

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob