Find the Derivative - d/dx y=12 square root of x

Problem

d()/d(x)*12√(,x)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to differentiate.

y=12*x(1/2)

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

d(y)/d(x)=12⋅1/2*x(1/2−1)

3. Simplify the coefficient and the exponent.

d(y)/d(x)=6*x(−1/2)

4. Convert the expression back into radical form by moving the negative exponent to the denominator.

d(y)/d(x)=6/√(,x)

Final Answer

(d(12)√(,x))/d(x)=6/√(,x)

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