Find the Derivative - d/dx (x^2)/8

Problem

d()/d(x)(x2)/8

Solution

1. Identify the constant factor in the expression. The expression (x2)/8 can be rewritten as 1/8⋅x2

2. Apply the constant multiple rule for derivatives, which states that d()/d(x)*[c⋅ƒ(x)]=c⋅d(ƒ(x))/d(x)

d()/d(x)(x2)/8=1/8⋅d(x2)/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) to differentiate x2

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

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

1/8⋅2*x=(2*x)/8

5. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 2.

(2*x)/8=x/4

Final Answer

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

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