Question

part 1)

Find the partial derivatives of the function f(x,y)=xsin(7x^6y):

fx(x,y)=

fy(x,y)=

part 2)

Find the partial derivatives of the function f(x,y)=x^6y^6/x^2+y^2

fx(x,y)=

fy(x,y)=

part 3)

Find all first- and second-order partial derivatives of the function f(x,y)=2x^2y^2−2x^2+5y

fx(x,y)=

fy(x,y)=

fxx(x,y)=

fxy(x,y)=

fyy(x,y)=

part 4)

Find all first- and second-order partial derivatives of the function f(x,y)=9ye^(3x)

fx(x,y)=

fy(x,y)=

fxx(x,y)=

fxy(x,y)=

fyy(x,y)=

part 5)

For the function given below, find the numbers (x,y) such that fx(x,y)=0 and fy(x,y)=0

f(x,y)=6x^2+23y^2+23xy+4x−2

Answer: x= and y=

part 6)

Find the following partial derivatives of the function f(x,y,z)=x^8+2yz^2+z^5

fx(x,y,z)=

fy(x,y,z)=

fz(x,y,z)=

fyz(x,y,z)=

Answer 1