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

Problem

d()/d(x)*(√(,x)+5/√(,x))

Solution

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

√(,x)+5/√(,x)=x(1/2)+5*x(−1/2)

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

d(x(1/2))/d(x)=1/2*x(−1/2)

(d(5)*x(−1/2))/d(x)=5⋅(−1/2)*x(−3/2)

3. Simplify the coefficients and the exponents.

1/2*x(−1/2)−5/2*x(−3/2)

4. Convert the expression back into radical form and positive exponents.

1/(2√(,x))−5/(2*x√(,x))

Final Answer

d()/d(x)*(√(,x)+5/√(,x))=1/(2√(,x))−5/(2*x√(,x))

Want more problems? Check here!