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

Mylo O'Moore

Mylo O'Moore

Answered question

2021-03-09

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

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-03-10Added 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

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