Find the Derivative - d/dx 4x^2+3

Problem

d()/d(x)*(4*x2+3)

Solution

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

d()/d(x)*(4*x2+3)=(d(4)*x2)/d(x)+d(3)/d(x)

2. Apply the constant multiple rule to the first term by pulling the constant 4 out of the derivative.

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

3. Apply the power rule to differentiate x2 where d(xn)/d(x)=n*x(n−1)

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

4*(2*x)=8*x

4. Apply the constant rule to the second term, noting that the derivative of any constant is 0

d(3)/d(x)=0

5. Combine the results to find the final derivative.

8*x+0=8*x

Final Answer

d()/d(x)*(4*x2+3)=8*x

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