Find the Derivative - d/dx square root of x+9/( square root of x)

Problem

d()/d(x)*(√(,x)+9/√(,x))

Solution

1. Rewrite the expression using power notation to make differentiation easier.

√(,x)+9/√(,x)=x(1/2)+9*x(−1/2)

2. Apply the sum rule for derivatives, which allows for differentiating each term separately.

d()/d(x)*(x(1/2)+9*x(−1/2))=d(x(1/2))/d(x)+(d(9)*x(−1/2))/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) to each term.

d(x(1/2))/d(x)=1/2*x(−1/2)

(d(9)*x(−1/2))/d(x)=9⋅(−1/2)*x(−3/2)

4. Simplify the coefficients and rewrite the expression using radical notation.

1/2*x(−1/2)−9/2*x(−3/2)=1/(2√(,x))−9/(2*x√(,x))

Final Answer

d()/d(x)*(√(,x)+9/√(,x))=1/(2√(,x))−9/(2*x√(,x))

Want more problems? Check here!