Question

Differentiate f(x) = (cosx^4)-(2x^2)

Answer 1

I will help you with this also.

Answer 2

:)

Answer 3

This is a long one, you have a product rule, and you also have a chain rule going on, so it may take a little bit for me to type up.

Answer 4

so your function is \[f(x)=-\cos(x^4)(2x^2)\] correct?

Answer 5

no

Answer 6

-cosine(x^4)(2x^2)?

Answer 7

f(x) = cosx^4-2x^2

Answer 8

ooh ok its cosine(x^4) MINUS 2x^2

Answer 9

and its not cosine(x ^4) x is the angle

Answer 10

Right, but you still have to differentiate the whole thing with respect to x. This is how you do it.

Answer 11

\[\frac{d}{dx}(\cos(x^4)-2x^2)=\frac{d}{dx}(\cos(x^4)) - 2\frac{d}{dx}(x^2)\]

Answer 12

Since you are taking the derivative of a sum, you can just break it up into the derivative of each individual term.

Answer 13

and on the second term, we can bring the -2 outside of the derivative because it is a constant.

Answer 14

The first derivative involves the chain rule. x first becomes x^4 and then gets shoved into a cosine function, so we must take the derivative of x^4 and multiply it by the derivative of something shoved into a cosine function:
\[\frac{d}{dx}\cos(x^4)=\frac{d}{dx}(x^4)\frac{d}{du}\cos(u)\]

Answer 15

where u is going to be x^4 at the end of this

Answer 16

so that gives \[-4x^3\sin(u)\]

Answer 17

or \[-4x^3\sin(x^4)\]

Answer 18

Combining this with the derivative of the other term gives the final answer:
\[-4x^3\sin(x^4)-4x\]

Answer 19

Factor a -4x out if you like:
\[-4x(x^2\sin(x^4)+1)\]

Answer 20

@ConradBarczyk you say "and its not cosine(x ^4) x is the angle "
so do you mean the problem is to find the derivative of\[\cos^4x-2x^2\]?or\[\cos(x^4)-2x^2\]

Answer 21

second one but patmayer1 answere it correctly and i think i can do the next one myself thanks :)

Answer 22

just making sure :)

Answer 23

thx