Find the Derivative - d/dx 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 constant multiple rule, which allows you to move the constant 7 outside the derivative.

d()/d(x)*7*x(−1/2)=7⋅d(x(−1/2))/d(x)

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

7⋅(−1/2*x(−1/2−1))=−7/2*x(−3/2)

4. Simplify the expression by moving the variable back to the denominator with a positive exponent.

−7/2*x(−3/2)=−7/(2*x(3/2))

Final Answer

d()/d(x)7/√(,x)=−7/(2*x√(,x))

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