Find the Derivative - d/d@VAR f(x)=x^2+2

Problem

d()/d(x)*(x^2+2)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=x^2+2

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives: d()/d(x)*(x^2+2)=d(x^2)/d(x)+d(2)/d(x)

3. Apply the power rule to the first term, where d(x^n)/d(x)=n*x^(n−1) For x^2 the derivative is 2*x

4. Apply the constant rule to the second term, where the derivative of any constant is 0 Thus, d(2)/d(x)=0

5. Simplify the resulting expression by adding the derivatives together.

Final Answer

d()/d(x)*(x^2+2)=2*x

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