Find the Derivative - d/d@VAR g(t)=4t^(-1/8)

Problem

d()/d(t)*4*t(−1/8)

Solution

1. Identify the function as a power function multiplied by a constant coefficient, where g(t)=4*t(−1/8)

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

3. Multiply the constant coefficient 4 by the exponent −1/8

d(g(t))/d(t)=4⋅(−1/8)*t(−1/8−1)

4. Simplify the coefficient by calculating 4⋅−1/8=−1/2

5. Subtract the exponents by calculating −1/8−8/8=−9/8

d(g(t))/d(t)=−1/2*t(−9/8)

Final Answer

(d(4)*t(−1/8))/d(t)=−1/2*t(−9/8)

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