Find the Derivative - d/dx y=-8/( cube root of x)

Problem

d()/d(x)*(−8/√(3,x))

Solution

1. Rewrite the expression using rational exponents to make it easier to differentiate.

y=−8*x(−1/3)

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

d(y)/d(x)=−8⋅(−1/3)*x(−1/3−1)

3. Simplify the coefficient by multiplying the constants.

d(y)/d(x)=8/3*x(−4/3)

4. Convert the expression back into radical form if necessary.

d(y)/d(x)=8/(3*x(4/3))

d(y)/d(x)=8/(3√(3,x4))

Final Answer

d()/d(x)*(−8/√(3,x))=8/(3*x(4/3))

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