Question

Encontre $\frac{\Delta f}{\Delta x} \: e \: \frac{\Delta f}{\Delta y}$ :

a) f(x,y)=$e^{-2y} cos(2xy)$

b) f(x,y)=$\sqrt{1-x^2-y^2}$

Answer 1

Resposta:

a)

f(x,y)=e^(-2y ) * cos(2xy)

fx=e^(-2y ) * [cos(2xy)]'

fx=e^(-2y) * (2xy)' * (-sen(2xy))

fx=e^(-2y) * (2y)*(-sen(2xy))

fx=(2y)*(-sen(2xy))  * e^(-2y)

fy=(-2y)' *e^(-2y) * cos(2xy)  + e^(-2y) * (2xy)' * [-sen(2xy)]

fy=-2 *e^(-2y) * cos(2xy)  + e^(-2y) * (2x) * [-sen(2xy)]

b)

f(x,y) =(1-x²-y²)^(1/2)

fx= (1/2) *(1-x²-y²)^(-1/2)  * (1-x²-y²)'

fx= (1/2) *(1-x²-y²)^(-1/2)  * (-2x)

fx=-x/√(1-x²-y²)

fy= (1/2) *(1-x²-y²)^(-1/2)  * (-2y)

fy= -y *(1-x²-y²)^(-1/2)

fy= -y/√(1-x²-y²)