Find the Derivative - d/dx y=7/( square root of x)

Problem

d()/d(x)7/√(,x)

Solution

1. Rewrite the expression using exponents to make it easier to differentiate.

7/√(,x)=7*x(−1/2)

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

(d(7)*x(−1/2))/d(x)=7⋅(−1/2)*x(−1/2−1)

3. Simplify the exponent and the coefficient.

−7/2*x(−3/2)

4. Convert the expression back into radical form with a positive exponent.

−7/(2*x(3/2))=−7/(2√(,x3))

Final Answer

d()/d(x)7/√(,x)=−7/(2*x√(,x))

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