Find the Derivative - d/dx 1/4x^2-1/2 natural log of x

Problem

d()/d(x)*(1/4*x2−1/2*ln(x))

Solution

1. Identify the expression as a difference of two terms and apply the sum/difference rule for derivatives.

d()/d(x)*(1/4*x2−1/2*ln(x))=d()/d(x)1/4*x2−d()/d(x)1/2*ln(x)

2. Apply the constant multiple rule to move the coefficients outside the derivatives.

1/4d(x2)/d(x)−1/2d(ln(x))/d(x)

3. Differentiate the first term using the power rule, where d(xn)/d(x)=n*x(n−1)

1/4*(2*x)=1/2*x

4. Differentiate the second term using the derivative rule for the natural logarithm, where d(ln(x))/d(x)=1/x

1/2*(1/x)=1/(2*x)

5. Combine the results to find the final derivative.

1/2*x−1/(2*x)

Final Answer

d()/d(x)*(1/4*x2−1/2*ln(x))=1/2*x−1/(2*x)

Want more problems? Check here!