Find the Derivative - d/dx 3xy

Problem

d()/d(x)*3*x*y

Solution

1. Identify the variables and constants. Here, 3 is a constant, x is the independent variable, and y is assumed to be a function of x denoted as y(x)

2. Apply the constant multiple rule to move the constant 3 outside of the derivative.

d()/d(x)*3*x*y=3(d(x)*y)/d(x)

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

3(d(x)*y)/d(x)=3*(xd(y)/d(x)+yd(x)/d(x))

4. Simplify the expression by evaluating the derivative of x with respect to x which is 1

3*(xd(y)/d(x)+y⋅1)

5. Distribute the constant 3 to both terms inside the parentheses.

3*xd(y)/d(x)+3*y

Final Answer

d()/d(x)*3*x*y=3*xd(y)/d(x)+3*y

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