Find the Derivative - d/dx 4xy

Problem

d()/d(x)*4*x*y

Solution

1. Identify the expression as a product of two functions of x where y is assumed to be a function of x denoted as y(x)

2. Apply the constant multiple rule to move the constant 4 outside of the derivative.

d()/d(x)*4*x*y=4d()/d(x)*x*y

3. Apply the product rule, which states d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x) letting u=x and v=y

4d()/d(x)*x*y=4*(xd(y)/d(x)+yd(x)/d(x))

4. Simplify the expression by noting that d(x)/d(x)=1

4*(xd(y)/d(x)+y(1))

5. Distribute the constant 4 to reach the final form.

4*xd(y)/d(x)+4*y

Final Answer

d()/d(x)*4*x*y=4*xd(y)/d(x)+4*y

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