Find the Derivative - d/dx f(x)=3 square root of x

Problem

d()/d(x)*3√(,x)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to apply the power rule.

√(,x)=x(1/2)

2. Apply the constant multiple rule, which allows the constant 3 to be moved outside the derivative.

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

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) where n=1/2

d(x(1/2))/d(x)=1/2*x(1/2−1)

4. Simplify the exponent by subtracting the values.

1/2−1=−1/2

5. Multiply the resulting expression by the constant 3

3⋅1/2*x(−1/2)=3/2*x(−1/2)

6. Rewrite the expression using positive exponents and radical notation.

3/(2√(,x))

Final Answer

(d(3)√(,x))/d(x)=3/(2√(,x))

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