Question

what is the derivative of sin(xy^2)

Answer 1

Assuming derivative with respect to x:
\[
\frac{d}{dx}\sin(xy^2) = \cos(xy^2) * \frac{d}{dx}(xy^2) =
\cos(xy^2) * \{x * 2y * \frac{dy}{dx} + 1 * y^2 \} = \\
2xy\cos(xy^2)\frac{dy}{dx} + y^2\cos(xy^2)
\]

Answer 2

Okay, thank you, I understand most of it, but I do have another question. How did you get the last {cos(xy^2)} that is with the y^2?

Answer 3

( sin(xy^2) )' = cos(xy^2) * (xy^2)'
Apply the product rule to find (xy^2)': x * 2yy' + 1*y^2
( sin(xy^2) )' = cos(xy^2) * (xy^2)' = cos(xy^2) * { x * 2yy' + 1*y^2 }
multiply it out: cos(xy^2) * x * 2yy' + cos(xy^2) * y^2 =
2xycos(xy^2)y' + y^2cos(xy^2)

Answer 4

I can't thank you enough, you are the best, thanks