Find the Derivative - d/dx 9xy

Problem

d()/d(x)*9*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 9 outside of the derivative.

d()/d(x)*9*x*y=9d()/d(x)*x*y

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

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

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

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

5. Distribute the constant 9 back into the result.

9*(xd(y)/d(x)+y)=9*xd(y)/d(x)+9*y

Final Answer

d()/d(x)*9*x*y=9*xd(y)/d(x)+9*y

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