Find the Derivative - d/dx (5 square root of x)/8

Problem

d()/d(x)(5√(,x))/8

Solution

1. Rewrite the expression by moving the constant coefficient 5/8 outside the derivative and converting the square root to a power.

d()/d(x)(5√(,x))/8=5/8d(x(1/2))/d(x)

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

d(x(1/2))/d(x)=1/2*x(1/2−1)

3. Simplify the exponent.

1/2*x(1/2−1)=1/2*x(−1/2)

4. Multiply the resulting derivative by the constant coefficient 5/8

5/8⋅1/2*x(−1/2)=5/16*x(−1/2)

5. Rewrite the expression using radical notation and moving the negative exponent to the denominator.

5/16*x(−1/2)=5/(16√(,x))

Final Answer

d()/d(x)(5√(,x))/8=5/(16√(,x))

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