Question

Prove that: dx(e^xy)=e^xy(y)

Answer 1

Is y a function of x?

Answer 2

Since here we are differentiate let hand side with respect to x

we have left hand sides is e^(xy) so here we use this rule of derivative

example d/dx (e^(ax)) = e^(ax) * a since we are differentiate with respect to x so in our example we will get d/dx (e^(xy) = e^(xy) * y

Answer 3

here y is coefficient of x

Answer 4

It seems y is a constant quantity and yes i agress with @tgawade

Answer 5

*agree

Answer 6

If A and B are the coefficients of the x and y and they are both equal to zero then C would always be equal to 0 for any given x and y value.
0x + 0y = 0.