Find the Derivative - d/dx 5x^(3/2)

Problem

d()/d(x)*5*x(3/2)

Solution

1. Identify the constant and the power of the variable in the expression 5*x(3/2)

2. Apply the constant multiple rule, which allows the constant 5 to be moved outside the derivative.

d()/d(x)*5*x(3/2)=5⋅d(x(3/2))/d(x)

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

d(x(3/2))/d(x)=3/2*x(3/2−1)

4. Simplify the exponent by subtracting the values.

3/2−1=1/2

5. Multiply the constant 5 by the result of the power rule.

5⋅3/2*x(1/2)=15/2*x(1/2)

Final Answer

d()/d(x)*5*x(3/2)=(15*x(1/2))/2

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