Find the Derivative - d/dx 2x^(3/2)

Problem

d()/d(x)*2*x^(3/2)

Solution

1. Identify the constant and the power of x in the expression. The expression is in the form c⋅x^n where c=2 and n=3/2

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

3. Multiply the constant by the exponent and subtract 1 from the exponent.

(d(2)*x^(3/2))/d(x)=2⋅3/2*x^(3/2−1)

4. Simplify the coefficient and the exponent.

2⋅3/2=3

3/2−1=1/2

Final Answer

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

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