若函数f(x,y,z)=[根号下(X^2+y^2)]e^3z,求df(3,-4,0)

Question

若函数 f(x,y,z)=[根号下(X^2+y^2)]e^3z,求df(3,-4,0)

Answer 1

f(x,y,z)=√(x²+y²)e^3z
f`x=x/√(x²+y²)e^3z=3/5
f`y=y/√(x²+y²)e^3z=-4/5
f`z=3√(x²+y²)e^3z=15
df(3,-4,0)=3/5dx-4/5dy+15dz