Find the Derivative - d/dx 3x^2y

Problem

d()/d(x)*3*x2*y

Solution

1. Identify the variables and constants. Since the derivative is with respect to x the term y is treated as a function of x requiring the use of the product rule.

2. Apply the product rule, which states that d()/d(x)*[ƒ(x)*g(x)]=ƒ(x)′*g(x)+ƒ(x)*g(x)′ Here, let ƒ(x)=3*x2 and g(x)=y

3. Differentiate the first part, 3*x2 with respect to x to get 6*x

4. Differentiate the second part, y with respect to x to get d(y)/d(x)

5. Combine the results using the product rule formula.

Final Answer

(d(3)*x2*y)/d(x)=6*x*y+3*x2d(y)/d(x)

Want more problems? Check here!