Find the Derivative - d/dx y=x^2+5x

Problem

d()/d(x)*(x2+5*x)

Solution

1. Identify the function to be differentiated, which is a sum of two terms: x2 and 5*x

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, x2 The derivative of xn is n*x(n−1) so the derivative of x2 is 2*x

4. Apply the constant multiple rule and the power rule to the second term, 5*x The derivative of a*x is a so the derivative of 5*x is 5

5. Combine the results to find the final derivative.

Final Answer

d(x2+5*x)/d(x)=2*x+5

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