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

Problem

d()/d(x)*x^(−2/5)

Solution

1. Identify the function as a power function of the form x^n where n=−2/5

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

3. Substitute the value of n into the power rule formula.

d(x^(−2/5))/d(x)=−2/5*x^(−2/5−1)

4. Simplify the exponent by subtracting the constants.

−2/5−1=−2/5−5/5=−7/5

5. Write the final derivative expression.

d(x^(−2/5))/d(x)=−2/5*x^(−7/5)

Final Answer

d(x^(−2/5))/d(x)=−2/5*x^(−7/5)

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