Find the Derivative - d/dx (x^3)/6

Problem

d()/d(x)(x3)/6

Solution

1. Identify the constant factor in the expression, which is 1/6

2. Apply the constant multiple rule of differentiation to move the constant outside the derivative.

d()/d(x)(x3)/6=1/6d(x3)/d(x)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to differentiate x3

d(x3)/d(x)=3*x2

4. Multiply the constant factor by the result of the derivative.

1/6⋅3*x2=(3*x2)/6

5. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 3.

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

Final Answer

d()/d(x)(x3)/6=(x2)/2

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