Find the Derivative - d/dx y=24 square root of x

Problem

d()/d(x)*24√(,x)

Solution

1. Rewrite the square root using a fractional exponent to prepare for the power rule.

y=24*x(1/2)

2. Apply the constant multiple rule, which allows the constant 24 to be moved outside the derivative.

d(y)/d(x)=24⋅d(x(1/2))/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) where n=1/2

d(y)/d(x)=24⋅1/2*x(1/2−1)

4. Simplify the coefficient and the exponent.

d(y)/d(x)=12*x(−1/2)

5. Rewrite the expression using a positive exponent and radical notation.

d(y)/d(x)=12/√(,x)

Final Answer

d()/d(x)*24√(,x)=12/√(,x)

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