Find the Derivative - d/dx 2x^(1/2)

Problem

d()/d(x)*2*x(1/2)

Solution

1. Identify the constant and the power of the variable x

2. Apply the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

d()/d(x)*2*x(1/2)=2d(x(1/2))/d(x)

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

2d(x(1/2))/d(x)=2⋅1/2*x(1/2−1)

4. Simplify the expression by multiplying the coefficients and subtracting the exponents.

2⋅1/2*x(−1/2)=1*x(−1/2)

5. Rewrite the expression using positive exponents if desired, noting that x(−1/2)=1/(x(1/2))

x(−1/2)=1/√(,x)

Final Answer

d()/d(x)*2*x(1/2)=1/√(,x)

Want more problems? Check here!