Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

Join Brainly to access

this expert answer

SEE EXPERT ANSWER

To see the **expert** answer you'll need to create a **free** account at **Brainly**

Is a a constant?

are you differentiating with respect to x..?

or a? :P .

Yes @campbell_st. I'm not sure @Dido525

That means a is a constant I assume O_o .

|dw:1352349392745:dw|

let u = a^3 + x^3 du/dx = 3x^2
let y = cos(u) du/dy = -sin (u)
so dy/dx = dy/du * du/dx

I can't see the rest.

One moment

\(\ \Huge -sinx(3a^2+3x^2) \)

then replace u with a^3 + x^3 for the final solution.

nope its
dy/dx = -sin(a^3 + x^3) * 3x^2

@campbell_st How did you get that?

Because a is a constant. The derivative of a constant is 0.

We multiply by the derivative of the inside part when using the chain rule.

and I used the chain rule..

the a^3 x^3 doesn't change

@campbell_st I thought a was a constant then? How does that stay the same?

Here:
|dw:1352349668500:dw|

We DO NOT change the inside.

|dw:1352349758941:dw|

Differentiate that.

With respect to x. Meaning a is a constant. We know the derivative of a constant is 0.

Usually letters a, b, and c are considered constants.

Well there are partial derivatives but you probably won't learn that now.

its just like
(x^2 + 3)^4 dy/dx = 4(x^2 + 3) ^3 *2x
the brackets don't change

you do... thats how you get 3x^2

But the term is still inside the parenthesis? That's really confusing me right now

parentheses*

|dw:1352350103544:dw|

Chain rule says d/dx(cos u)= -sin u (u')

yep and du/dx = u'
you are differentiating u with respect to x

So u= a^3 + x^3

U'= 0 + 3x^2

Ok well u know d/dx of cos x= -sin x right?

The expression inside of the expression on the outside ALWAYS remains. It's just how it is.

\(\ \text{Yes!} \)

"on the outside"?

Okay\(\ \text{...} \)

Angle measure?