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

Problem

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

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

2. Apply the power rule to the first term, where d(xn)/d(x)=n*x(n−1)

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

3. Apply the constant multiple rule and the power rule to the second term.

(d(3)*x)/d(x)=3

4. Combine the results to find the final derivative.

2*x+3

Final Answer

d()/d(x)*(x2+3*x)=2*x+3

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