Question

partial derivatives of xSin(yz)

Answer 1

So if we're just doing partial deriviatves, then we choose to differentiate with respect to one variable while pretending all the other variables are constants. So if we start with respect to x we get

sin(yz)

The entirety of sin(yz) is just a constant, so we merely drop x and leave that behind. Now if we differentiate with respect to y, treating x and z as constants we would get

xzcos(yz).

This was a chain rule. The derivative of sin is just cos, then we multiply by the derivative of the inner function yz. Since z is just a constant, we drop y and are left with only z to multiply. Now finally if we differentiate with respect to z, we would have

xycos(yz)

This was the same thing as the derivative with respect to y, but instead y was the constant and z was the variable expression. Otherwise everything was the same. So these would be your 3 partial derivatives. Any of that make sense? ^_^

Answer 2

thank you ^^

Answer 3

Yep, np ^_^