Find the Derivative - d/dd d/(dx)*(4x^2)+7x- natural log of x

Problem

d()/d(x)*(4*x2+7*x−ln(x))

Solution

1. Identify the expression to be differentiated, which is a sum of three terms: 4*x2 7*x and −ln(x)

2. Apply the power rule to the first term, 4*x2 which states that d(xn)/d(x)=n*x(n−1)

(d(4)*x2)/d(x)=8*x

3. Apply the power rule to the second term, 7*x

(d(7)*x)/d(x)=7

4. Apply the derivative rule for the natural logarithm, which states that d(ln(x))/d(x)=1/x

(d(−)*ln(x))/d(x)=−1/x

5. Combine the results of the individual derivatives using the sum rule.

d()/d(x)*(4*x2+7*x−ln(x))=8*x+7−1/x

Final Answer

d()/d(x)*(4*x2+7*x−ln(x))=8*x+7−1/x

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