Find the Derivative - d/dx y=(5 square root of x)/6

Problem

d()/d(x)(5√(,x))/6

Solution

1. Rewrite the expression by moving the constant coefficient outside and converting the square root to an exponent using the rule √(,x)=x(1/2)

d()/d(x)5/6*x(1/2)

2. Apply the constant multiple rule, which allows the constant 5/6 to be moved in front of the derivative operator.

5/6d(x(1/2))/d(x)

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

5/6⋅1/2*x(1/2−1)

4. Simplify the exponent and multiply the fractions.

5/12*x(−1/2)

5. Rewrite the expression using positive exponents and radical notation by applying the rule x(−1/2)=1/√(,x)

5/(12√(,x))

Final Answer

d()/d(x)(5√(,x))/6=5/(12√(,x))

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