Question

Derivative of x^3cos3x^2

Answer 1

3x^2cos(3x^2)-6x^4sin(3x^2)x

Answer 2

@jamalahmed2068, can you explain how you got that answer

Answer 3

do you know product rule???
(uv)'=u'v+uv'
just use this..

Answer 4

Yes. Do you need to use the chain rule?

Answer 5

yes you have to use chain rule for the derivative of cos(x^2)

Answer 6

How come? Is it necessary for any Trig. function drivative?

Answer 7

y=cos(x^2)
let u=x^2
du=2xdx
y=cos(u)
dy=-sin(u)du
so dy=-2xsin(x^2)dx

Answer 8

not always!!
chain rule
dy/du=(dy/dx) (dx/du)
got it!!

Answer 9

chain rule is used when functions are composed....(do you know the the composition of functions)

Answer 10

Is it the f(g(x)) type

Answer 11

f(x)=cos(x)
g(x)=x^2
fog=cos(x^2)

Answer 12

let f and g are functions of x
y=f(g(x))
let u=g
y=f(u)
dy/dx=d(f(u))/du du/dx
=f'(u)du/dx
=f'(g(x)) g'(x)
got it nowww