Find the Derivative - d/dx 6x^(1/2)

Problem

d()/d(x)*6*x(1/2)

Solution

1. Identify the constant and the power of x in the expression 6*x(1/2)

2. Apply the power rule for differentiation, which states that d()/d(x)*a*xn=n⋅a*x(n−1)

3. Multiply the exponent 1/2 by the coefficient 6

1/2⋅6=3

4. Subtract 1 from the exponent 1/2

1/2−1=−1/2

5. Simplify the resulting expression into its final form.

Final Answer

(d(6)*x(1/2))/d(x)=3*x(−1/2)

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