Find the Derivative - d/dx f(x)*(2x^2)

Problem

d()/d(x)*ƒ(x)⋅2*x2

Solution

1. Identify the rule needed for the derivative of a product of two functions, which is the product rule.

2. Apply the formula for the product rule, which states d()/d(x)*u⋅v=u⋅d(v)/d(x)+v⋅d(u)/d(x)

3. Assign the functions u=ƒ(x) and v=2*x2

4. Differentiate each part separately to find d(ƒ(x))/d(x)=ƒ(x)′ and (d(2)*x2)/d(x)=4*x

5. Substitute these derivatives back into the product rule formula.

6. Simplify the resulting expression by rearranging the terms.

Final Answer

d()/d(x)*ƒ(x)⋅2*x2=2*x2*ƒ(x)′+4*x*ƒ(x)

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