# Thread: Another Chain Rule Question.

1. ## Another Chain Rule Question.

$f(x)= sin^4(x)$

What does 'u' in this situation equal?

$sin(x)$or $x^4$

2. ## d/dx(x^n)=nx^(n-1)dx/dx

Originally Posted by Zanderist
$f(x)= sin^4(x)$

What does 'u' in this situation equal?

$sin(x)$or $x^4$
f'(x)=4sin^3xcosx

the chain rule is a mere technical jargon!

3. Originally Posted by Zanderist
$f(x)= sin^4(x)$

What does 'u' in this situation equal?

$sin(x)$or $x^4$
u is always the "internal" function. Here, to evaluate $sin^4(x)$ you would first evaluate sin(x) then take the fourth power. If you let u= sin(x) then $f(x)= u^4$

4. I'd like to add on to this.

What are the steps to:

$f(x)=7cos(cos(x))$

5. Originally Posted by Zanderist
I'd like to add on to this.

What are the steps to:

$f(x)=tan 4x$
$\frac{d}{dx} \tan{u} = \sec^2{u} \cdot \frac{du}{dx}
$

... in future, start a new problem with a new thread.

more examples of the chain rule ...

http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html

6. Originally Posted by Zanderist
I'd like to add on to this.

What are the steps to:

$f(x)=7cos(cos(x))$
$f(x) = 7\cos{u}$

$f'(x) = -7\sin{u} \cdot \frac{du}{dx}$