Find the Derivative - d/dx y=8 square root of x

Problem

d()/d(x)*8√(,x)

Solution

1. Rewrite the square root 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 8 to be moved outside the derivative.

(d(8)*x(1/2))/d(x)=8⋅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 multiply the constants.

8⋅1/2*x(−1/2)=4*x(−1/2)

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

4*x(−1/2)=4/(x(1/2))=4/√(,x)

Final Answer

d()/d(x)*8√(,x)=4/√(,x)

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