Question

Find the a derivative 4 cos x sin y = 1:

a) − cos(x) / sin(y)
b) sin(x)/cos(y)
c) cos(x)/sin(y)
d) −sin(x)/cos(y)

Answer 1

The derivative of 4 cos(x) sin(y) = 1 is -4 sin(x) sin(y) with respect to x and 4 cos(x) cos(y) with respect to y.

Step-by-step explanation:

To find the derivative of 4 cos(x) sin(y) = 1, we need to differentiate each term with respect to x and y separately using the product rule.

Derivative with respect to x:

d/dx(4 cos(x) sin(y)) = -4 sin(x) sin(y)

Derivative with respect to y:

d/dy(4 cos(x) sin(y)) = 4 cos(x) cos(y)

Therefore, the derivative of 4 cos(x) sin(y) = 1 with respect to x is -4 sin(x) sin(y) and with respect to y is 4 cos(x) cos(y).