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

Problem

d()/d(x)(5√(,x))/6

Solution

1. Rewrite the expression by moving the constant coefficient outside the derivative and converting the radical to a power.

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

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

5/6⋅1/2*x(1/2−1)

3. Simplify the exponent and multiply the fractions.

5/12*x(−1/2)

4. Rewrite the expression using positive exponents and radical notation.

5/(12√(,x))

Final Answer

d()/d(x)(5√(,x))/6=5/(12√(,x))

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