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

Problem

d()/d(x)*x√(,x)

Solution

1. Rewrite the expression using exponent notation by converting the square root to a power of 1/2

ƒ(x)=x1⋅x(1/2)

2. Simplify the expression by adding the exponents according to the product rule for exponents.

ƒ(x)=x(3/2)

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

d(x(3/2))/d(x)=3/2*x(3/2−1)

4. Subtract the exponents to find the final power.

d(x(3/2))/d(x)=3/2*x(1/2)

5. Convert the exponent back into radical form for the final result.

d(x(3/2))/d(x)=(3√(,x))/2

Final Answer

(d(x)√(,x))/d(x)=(3√(,x))/2

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