Math Is Fun Forum

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