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

Problem

d()/d(x)*(3*x(2/3)−2*x)

Solution

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

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

2. Apply the constant multiple rule to move the constants outside of the derivatives.

3d(x(2/3))/d(x)−2d(x)/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to both terms.

3⋅2/3*x(2/3−1)−2⋅1*x(1−1)

4. Simplify the exponents and coefficients by performing the subtraction and multiplication.

2*x(−1/3)−2

5. Rewrite the expression using positive exponents if desired, noting that x(−1/3)=1/(x(1/3))

2/(x(1/3))−2

Final Answer

d()/d(x)*(3*x(2/3)−2*x)=2/(x(1/3))−2

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