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

Problem

d()/d(x)*2*x2*y

Solution

1. Identify the variables involved, noting that y is typically treated as a function of x (implicit differentiation) or as a constant if specified. Assuming y is a function of x we must use 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)=2*x2 and g(x)=y

3. Differentiate the first part, 2*x2 with respect to x using the power rule.

(d(2)*x2)/d(x)=4*x

4. Differentiate the second part, y with respect to x

d(y)/d(x)=d(y)/d(x)

5. Combine the results using the product rule formula.

4*x⋅y+2*x2⋅d(y)/d(x)

Final Answer

d()/d(x)*2*x2*y=4*x*y+2*x2d(y)/d(x)

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