Evaluate

[CatchThis2]

What is f ' (x) ?

Is it cos x^6/6 ?

 

[galactus]

F(x) is called the antiderivative of f(x).

\(\displaystyle F(x)=\int f(x)\)

So, what is the derivative of \(\displaystyle \int f(x)dx\)?.

That is, what is \(\displaystyle \frac{d}{dx}[F(x)]=\frac{d}{dx}\int f(x)dx=\)

What happens when you differentiate an antiderivative?.


Besides, \(\displaystyle \int sin(x^{5})dx\) is a nasty integration that is beyond elementary calc.

The point is not to integrate, but use the basic knowledge of what an antiderivative is.

 

[CatchThis2]

Simplified the problem to (cosx)(5x^4)

f '(x)= (cosx^5) (5x^4)

 

[galactus]

You just found the derivative of f(x), not F(x).

 

[CatchThis2]

Sorry for the confusion, the question is asking me to find f '(x)

 

[galactus]

Oh, OK then. That is a different matter. In that case, your last post is correct.

Remember, F(x) normally means the ANTI-derivative. As in integration. If you are not there yet, you will learn about it later.

 

[CatchThis2]

The integral of sin(x^5)dx

The f '(x)= (cosx^5) (5x^4) Correct ?

 

[Deleted member 4993]

The integral of sin(x^5)dx <<<< Where did this come from?

The f '(x)= (cosx^5) (5x^4) Correct ?

If

f(x) = sin (x[sup:3lujo3hg]5[/sup:3lujo3hg])

then, using chain rule

f'(x) = cos(x[sup:3lujo3hg]5[/sup:3lujo3hg]) * 5 * x[sup:3lujo3hg]4[/sup:3lujo3hg] = 5 * x[sup:3lujo3hg]4[/sup:3lujo3hg] * cos(x[sup:3lujo3hg]5[/sup:3lujo3hg])