Find the Derivative - d/dt ((2t+1)^(3/2))/3

Problem

d()/d(t)((2*t+1)(3/2))/3

Solution

1. Identify the constant factor and move it outside the derivative.

1/3d(2*t+1)/d(t)

2. Apply the power rule and the chain rule to the expression (2*t+1)(3/2)

1/3⋅3/2*(2*t+1)(3/2−1)⋅d(2*t+1)/d(t)

3. Differentiate the inner function 2*t+1 with respect to t

d(2*t+1)/d(t)=2

4. Substitute the derivative of the inner function back into the expression.

1/3⋅3/2*(2*t+1)(1/2)⋅2

5. Simplify the coefficients by canceling the common factors.

3/6⋅2*(2*t+1)(1/2)

1/2⋅2*(2*t+1)(1/2)

(2*t+1)(1/2)

Final Answer

d()/d(t)((2*t+1)(3/2))/3=√(,2*t+1)

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