# Another Chain Rule Question.

• Mar 10th 2010, 09:58 PM
Zanderist
Another Chain Rule Question.
$f(x)= sin^4(x)$

What does 'u' in this situation equal?

$sin(x)$or $x^4$
• Mar 10th 2010, 10:07 PM
Pulock2009
d/dx(x^n)=nx^(n-1)dx/dx
Quote:

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!
• Mar 11th 2010, 04:41 AM
HallsofIvy
Quote:

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 $f(x)= u^4$
• Mar 13th 2010, 03:44 PM
Zanderist
I'd like to add on to this.

What are the steps to:

$f(x)=7cos(cos(x))$
• Mar 13th 2010, 03:50 PM
skeeter
Quote:

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
• Mar 13th 2010, 04:31 PM
skeeter
Quote:

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

What are the steps to:

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

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

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