Find all the first and second order partial derivatives of f(x, y) = -7 sin (2x

Question

Find all the first and second order partial derivatives of f(x, y) = -7 sin (2x + y) - 6 cos(x - y). partial differential f/partial differential x = f_x = ________ partial differential f/partial differential y = f_y = ________ partial differential^2 f/partial differential x^2 = f_xx = ________ partial differential^2 f/partial differential y^2 = f_yy = ________ partial differential^2 f/partial differential x partial differential y = f_yx = ________ partial differential^2 f/partial differential y partial differential x = f_xy = ________

Explanation / Answer

f(x,y)=-7sin(2x+y)-6cos(x-y)

A)

fx=(-7(cos(2x+y))(2+0))-(6(-sin(x-y))(1-0))

fx=-14cos(2x+y) +6sin(x-y)

B)

fy=(-7(cos(2x+y))(0+1))-(6(-sin(x-y))(0-1))

fy=-7cos(2x+y) -6sin(x-y)

C)

fx=-14cos(2x+y) +6sin(x-y)

fxx=(-14(-sin(2x+y))(2+0)) +(6(cos(x-y))(1-0))

fxx=28sin(2x+y) +6(cos(x-y)

D)

fy=-7cos(2x+y) -6sin(x-y)

fyy=(-7(-sin(2x+y))(0+1)) -(6(cos(x-y))(0-1))

fyy=7sin(2x+y) +6cos(x-y)

E)

fy=-7cos(2x+y) -6sin(x-y)

fyx=(-7(-sin(2x+y))(2+0)) -(6(cos(x-y))(1-0))

fyx=14sin(2x+y) -6cos(x-y)

F)

fx=-14cos(2x+y) +6sin(x-y)

fxy=(-14(-sin(2x+y))(0+1)) +(6(cos(x-y))(0-1))

fxy=14sin(2x+y) -6cos(x-y)

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