Find the Derivative - d/dx -3x^2+54 natural log of x

Problem

d()/d(x)*(−3*x^2+54*ln(x))

Solution

1. Identify the derivative of the sum as the sum of the derivatives using the linearity rule.

d()/d(x)*(−3*x^2+54*ln(x))=(d(−)*3*x^2)/d(x)+(d(54)*ln(x))/d(x)

2. Apply the power rule to the first term, where the derivative of a*x^n is a*n*x^(n−1)

(d(−)*3*x^2)/d(x)=−6*x

3. Apply the derivative rule for the natural logarithm to the second term, where d(ln(x))/d(x)=1/x

(d(54)*ln(x))/d(x)=54⋅1/x

4. Combine the results of the derivatives into a single expression.

−6*x+54/x

Final Answer

d()/d(x)*(−3*x^2+54*ln(x))=−6*x+54/x

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