Question

Find the Derivative, using Chain Rule.
y=6x^2+5cosx

Answer 1

Since you say use the chain rule, does that mean you really have: \[\LARGE y=6x^{2+5\cos x}\]

Answer 2

eheh... I don't see much chain ruling there, unless is an exponentional or otherwise

Answer 3

Which is why I'm asking...

Answer 4

My Mistake,
\[y=6x^2+5cosx\]

Answer 5

You are right there is no chain rule

Answer 6

the only thing I can see chain-ruling would be the \(x^2\) and the cos(x)

other than that.... is just a constant in front

Answer 7

so.. chain-rule those 2 I gather....

Answer 8

6x^2 is done by the power rule.

Answer 9

So, it would be 12x, but what about the 5cosx?

Answer 10

What is the derivative of cos(x)?

Answer 11

-sin?

Answer 12

so it would be -5sinx?

Answer 13

Yes

Answer 14

well... one could say \(\bf 6\cdot \cfrac{d}{dx}[x^2]\cdot \cfrac{d}{dx}[x]\implies 6\cdot 2x^1\cdot 1x^0\implies 12x\)

Answer 15

so my answer is
12x+-sin5x?

Answer 16

well... you don't really need the chain-rule per se
but I gather the exercise is to use it

Answer 17

but yes... is 12x-5sin(x)

Answer 18

to say chain-rule the cos(x) part... one could \(\bf 5cos(x)\implies 5\cdot \cfrac{d}{dx}[cos(x)]\cdot \cfrac{d}{dx}[x]\)

Answer 19

Okay Thank You (: