Find the Derivative - d/dx 3x^2-2cos(x)

Problem

d()/d(x)*(3*x2−2*cos(x))

Solution

1. Apply the sum rule for differentiation, which allows for the derivative of each term to be taken individually.

d()/d(x)*(3*x2−2*cos(x))=(d(3)*x2)/d(x)−(d(2)*cos(x))/d(x)

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

(d(3)*x2)/d(x)=3*(2*x)=6*x

3. Apply the trigonometric rule to the second term, noting that d(cos(x))/d(x)=−sin(x)

(d(2)*cos(x))/d(x)=2*(−sin(x))=−2*sin(x)

4. Combine the results and simplify the signs.

6*x−(−2*sin(x))=6*x+2*sin(x)

Final Answer

d()/d(x)*(3*x2−2*cos(x))=6*x+2*sin(x)

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