Find the Derivative - d/dt 860-326/( square root of t)

Problem

d()/d(t)*(860−326/√(,t))

Solution

1. Rewrite the expression using power notation to make differentiation easier, noting that √(,t)=t(1/2) and 1/(t(1/2))=t(−1/2)

d()/d(t)*(860−326*t(−1/2))

2. Apply the sum rule for derivatives, which allows for the differentiation of each term independently.

d(860)/d(t)−(d(326)*t(−1/2))/d(t)

3. Differentiate the constant term 860 which results in 0

0−(d(326)*t(−1/2))/d(t)

4. Apply the power rule d(tn)/d(t)=n*t(n−1) to the second term, multiplying the coefficient by the exponent.

−326⋅(−1/2)*t(−1/2−1)

5. Simplify the coefficients and the exponent.

163*t(−3/2)

6. Convert the expression back into radical form for the final result.

163/(t(3/2))

Final Answer

d()/d(t)*(860−326/√(,t))=163/(t√(,t))

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