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

Problem

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

Solution

1. Identify the expression as a sum of two terms, x^3 and x

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

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

3. Apply the power rule to the first term, where d(x^n)/d(x)=n*x^(n−1) For x^3 n=3

d(x^3)/d(x)=3*x^2

4. Apply the power rule to the second term. For x n=1

d(x)/d(x)=1*x^0=1

5. Combine the results of the derivatives.

3*x^2+1

Final Answer

d()/d(x)*(x^3+x)=3*x^2+1

Want more problems? Check here!