derivative !!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

Answer 1

1) Given that z = 6ye^5x

Differentiate with respect to x we get,

d/dx(z) = d/dx(6ye^5x)                               

            = 6ye^5x d/dx(5x)         [Since d/dx(e^x) = e^x]

            = 6ye^5x (5)                [Since d/dx(ax) = a]

            = 30ye^5x

Differentiate with respect to x we get,

d^2/dx^2(z) = d/dx(30ye^5x)

                 = 30ye^5x d/dx(5x)  [Since d/dx(e^x) = e^x]

                 = 30ye^5x (5)         [Since d/dx(ax) = a]

                 = 150ye^5x

2) Given that z = 6ye^5x

Differentiate with respect to y we get,

d/dy(z) = d/dy(6ye^5x)                               

            = 6e^5x                       [Since d/dy(ay) = a]

Differentiate with respect to y we get,

d^2/dy^2(z) = d/dy(6e^5x)

                  = 0                       [Since d/dy(a) =0]

3) Given that z = 6ye^5x

Differentiate with respect to x we get,

d/dx(z) = d/dx(6ye^5x)                               

           = 6ye^5x d/dx(5x)         [Since d/dx(e^x) = e^x]

           = 6ye^5x (5)                [Since d/dx(ax) = a]

           = 30ye^5x

Differentiate with respect to y we get,

And z = 6ye^5x

Differentiate with respect to y we get,

d/dy(z) = d/dy(6ye^5x)                               

            = 6e^5x                      [Since d/dy(ay) = a]

Differentiate with respect to x we get,