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

Problem

d()/d(x)*(x^2+5)

Solution

1. Identify the rule for differentiation, which is the sum rule: the derivative of a sum is the sum of the derivatives.

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

2. Apply the power rule to the first term x^2 which states that d(x^n)/d(x)=n*x^(n−1)

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

3. Apply the constant rule to the second term 5 which states that the derivative of any constant is zero.

d(5)/d(x)=0

4. Combine the results of the derivatives.

2*x+0=2*x

Final Answer

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

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