Find the Derivative - d/dt 699/((t+1)^0.94)

Problem

d()/d(t)699/((t+1)0.94)

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

699/((t+1)0.94)=699*(t+1)(−0.94)

2. Apply the power rule and the chain rule by multiplying the constant by the exponent and subtracting 1 from the exponent.

d()/d(t)*699*(t+1)(−0.94)=699⋅(−0.94)*(t+1)(−0.94−1)⋅d(t+1)/d(t)

3. Calculate the product of the constants and the new exponent value.

699⋅(−0.94)=−657.06

−0.94−1=−1.94

4. Simplify the expression by noting that the derivative of t+1 with respect to t is 1.

−657.06*(t+1)(−1.94)⋅1=−657.06*(t+1)(−1.94)

5. Convert the result back into fraction form with a positive exponent.

−657.06*(t+1)(−1.94)=−657.06/((t+1)1.94)

Final Answer

d()/d(t)699/((t+1)0.94)=−657.06/((t+1)1.94)

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