Find ds/dt s=(11t-t^2)^(2/3)

Problem

d()/d(t)*(11*t−t2)(2/3)

Solution

1. Identify the outer and inner functions to apply the Chain Rule. The outer function is u(2/3) and the inner function is u=11*t−t2

2. Differentiate the outer function with respect to u using the Power Rule.

d(u(2/3))/d(u)=2/3*u(−1/3)

3. Differentiate the inner function with respect to t

d(11*t−t2)/d(t)=11−2*t

4. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function.

d(s())/d(t)=2/3*(11*t−t2)(−1/3)⋅(11−2*t)

5. Simplify the expression by moving the negative exponent to the denominator.

d(s())/d(t)=(2*(11−2*t))/(3*(11*t−t2)(1/3))

Final Answer

d(s())/d(t)=(22−4*t)/(3√(3,11*t−t2))

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