SOLUTION: I'd be very greatful if you could help me with this question in partial derivatives. Find the first partial derivatives of a. h(x,y) = e^ −(x2+y2) b. 𝑧 = &#119

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: I'd be very greatful if you could help me with this question in partial derivatives. Find the first partial derivatives of a. h(x,y) = e^ −(x2+y2) b. 𝑧 = &#119      Log On


   

Question 1085901: I'd be very greatful if you could help me with this question in partial derivatives.
Find the first partial derivatives of
a. h(x,y) = e^ −(x2+y2)
b. 𝑧 = 𝑒^(𝑦) sin𝑥𝑦
p.s : i'm pretty sure this question comes under the category I chose so please excuse that :)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%2Cy%29+=+e%5E%28-%28x%5E2%2By%5E2%29%29++
apply the exponential function rule: %28e%5E%28u%28x%29%29%29’=e%5E%28u%28x%29%29*u’%28x%29
%28d%2Fd%5Bx%5D%29%28+e%5E%28-%28x%5E2%2By%5E2%29%29+%29
= e%5E%28-%28x%5E2%2By%5E2%29%29%2A%28d%2Fd%5Bx%5D%29%28-%28x%5E2%2By%5E2%29%29
= e%5E%28-%28x%5E2%2By%5E2%29%29%2A%28d%2Fd%5Bx%5D%29%28-x%5E2-y%5E2%29
=
= e%5E%28-%28x%5E2%2By%5E2%29%29%2A%280-2x%29
=+-2x%2Ae%5E%28-%28x%5E2%2By%5E2%29%29

2.
z=e%5E%28y%29+sin%28xy%29+:
%28d%2Fd%5Bx%5D%29%28e%5E%28y%29+sin%28xy%29%29
=e%5E%28y%29+%28d%2Fd%5Bx%5D%29%28+sin%28xy%29%29
=e%5E%28y%29+%2Acos%28xy%29%28d%2Fd%5Bx%5D%29%28+xy%29
=y%2A%28d%2Fd%5Bx%5D%29%2Ae%5E%28y%29+cos%28xy%29
=1%2Ay%2Ae%5E%28y%29+cos%28xy%29
=ye%5E%28y%29+cos%28xy%29