Find the Derivative - d/dx y=18 square root of x

Problem

d()/d(x)*18√(,x)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to apply the power rule.

√(,x)=x(1/2)

2. Apply the constant multiple rule, which allows the constant 18 to be moved outside the derivative.

(d(18)*x(1/2))/d(x)=18⋅d(x(1/2))/d(x)

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

d(x(1/2))/d(x)=1/2*x(1/2−1)

4. Simplify the exponent and the coefficient.

1/2*x(−1/2)

5. Multiply by the constant 18 and rewrite with a positive exponent.

18⋅1/2*x(−1/2)=9*x(−1/2)

6. Convert the expression back into radical form.

9*x(−1/2)=9/√(,x)

Final Answer

(d(18)√(,x))/d(x)=9/√(,x)

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