Find the Derivative - d/dx f(x)=2 square root of x

Problem

d()/d(x)*2√(,x)

Solution

1. Rewrite the square root as a fractional exponent to prepare for differentiation.

ƒ(x)=2*x(1/2)

2. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) and use the constant multiple rule.

(d(2)*x(1/2))/d(x)=2⋅1/2*x(1/2−1)

3. Simplify the coefficients and the exponent.

(d(2)*x(1/2))/d(x)=1*x(−1/2)

4. Convert the negative exponent back into a radical form in the denominator.

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

(d(2)*x(1/2))/d(x)=1/√(,x)

Final Answer

(d(2)√(,x))/d(x)=1/√(,x)

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