Find the first partial derivatives of the following functions. f(x,y)=xe^y

Mylo O'Moore 2021-03-09 Answered
Find the first partial derivatives of the following functions. f(x,y)=xey
You can still ask an expert for help

Want to know more about Derivatives?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

jlo2niT
Answered 2021-03-10 Author has 96 answers
Step 1
To find the first-order partial derivatives of the function,
f(x,y)=xey
Step 2
The partial derivatives with respect to x is given by,
fx(x,y)=limh0f(x+h,y)f(x,y)h=limh0(x+h)eyxeyh=limh0xey+heyxeyh=limh0heyh
=limh0ey=ey
The partial derivatives with respect to y is given by,
fy(x,y)=limk0f(x,y+k)f(x,y)h=limk0xey+kxeyk=limk0xey(ek1)k=xeylimk0ek1k
=xeylimk0ek=xey(1)=xey
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more