Find the Derivative - d/dx y=4/( square root of x)

Problem

d()/d(x)4/√(,x)

Solution

1. Rewrite the expression using exponents to make it easier to differentiate, noting that √(,x)=x(1/2) and moving it to the numerator makes the exponent negative.

y=4*x(−1/2)

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

d(y)/d(x)=4⋅(−1/2)*x(−1/2−1)

3. Simplify the coefficient and the exponent.

d(y)/d(x)=−2*x(−3/2)

4. Convert the expression back into radical form by moving the variable to the denominator.

d(y)/d(x)=−2/(x(3/2))

d(y)/d(x)=−2/√(,x3)

Final Answer

d()/d(x)4/√(,x)=−2/(x√(,x))

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