Question

Find Gradient at point V= exp(2x+3y)cos5z, 0.1, -0.2, 0.4)

Answer 1

Do you know how to find the gradient? It's really just denoted by this little upside down delta (called a Nabla or Del symbol) and usually has a bar on top of it to show that it turns scalar functions into vector functions: Here it is: \[\LARGE \bar \nabla V = \frac{\partial V}{\partial x} \hat i +\frac{\partial V}{\partial y} \hat j +\frac{\partial V}{\partial z} \hat k\]

Answer 2

Do I need to seperate the e(2x+3y) into e^(2x)e^(3y)? if not.
I have 2e^(2x+3y)i + 3e^(2x+3y)j -5sin5z. Is it right?

Answer 3

You only need to use the chain rule and consider everything that's not your current variable a constant, so for instance: \[\LARGE \frac{\partial}{\partial y}\left(e^{(2x+3y)} \right)=3e^{(2x+3y)}\] since the derivative of 2x with respect to y is 0 and the derivative of 3y with respect to y is 3.

So you're totally right, that method you used works just as well, but that's slightly more general, I hope that helps.

One last thing, you forgot to multiply e^(2x+3) on your last component. It's still jut a constant coefficient in front of sin(5z) so it will stay there.

Answer 4

oh yeah...ok thanks