Find the Derivative - d/dx 8x^(1/2)

Problem

d()/d(x)*8*x(1/2)

Solution

1. Identify the constant and the power of x in the expression.

2. Apply the constant multiple rule, which states that d()/d(x)*[c*ƒ(x)]=cd()/d(x)*ƒ(x)

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

4. Multiply the constant 8 by the exponent 1/2

8⋅1/2=4

5. Subtract 1 from the exponent 1/2

1/2−1=−1/2

6. Combine the results to find the derivative.

Final Answer

(d(8)*x(1/2))/d(x)=4*x(−1/2)

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