Derivative of y=cos(xy)
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- Опубликовано: 16 сен 2024
- To find the derivative of this function, you'll need implicit differentiation.
derivative of y is just y'
derivative of cos(xy) requires chain rule AND product rule. It's -sin(xy)*(y+xy')
After taking this derivative, you'll need to multiply the -sin(xy) through the brackets (distribute) and then collect terms that contain y' on the one side of the equation. Then factor, and isolate y' with division.
Good intuitive thoughts spoken aloud
Nice video! Just have a few observations:
a) It would be fun to write the function y as:
y = cos(xcos(xcos(xcos(....... )...)
b) We can also use the multivariate chain rule to do essentially the same as what u did:
df(x,y) = (∂f/∂x) dx + (∂f/∂y) dy. In this example, with f(x,y) = cos(xy),
==> 1 = (∂f/∂x) (1/y') + (∂f/∂y) = [-ysin(xy)]/y' - xsin(xy)
==> 1/y' = [1+ xsin(xy)] / [-ysin(xy)] , giving the same answer you got
Nice video ❤
I wonder, would this question be the same as asking:
Find the derivative of y for
y = cos(xcos(xcos(xcos(x…))))? Going infinitely
no as it's a equation not a identity
Should note the domain of y is relative to the x given (arccos(y)/y)=x.
lovely