Find the Derivative - d/d@VAR f(x)=2x^2+1

Problem

d()/d(x)*(2*x2+1)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=2*x2+1

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

3. Apply the power rule to the first term, 2*x2 The power rule states that d(xn)/d(x)=n*x(n−1)

(d(2)*x2)/d(x)=2⋅2*x(2−1)

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

4. Apply the constant rule to the second term, 1 The derivative of any constant is 0

d(1)/d(x)=0

5. Combine the results of the derivatives.

4*x+0=4*x

Final Answer

d()/d(x)*(2*x2+1)=4*x

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