Problem 15

Question

Find the derivative of the function. $$ s(t)=t^{3}-2 t+4 $$

Step-by-Step Solution

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Answer

The derivative of the function $ s(t) = t^3 - 2t + 4 $ is $ ds/dt = 3*t^2 -2 $.

1Step 1: Identify the function

The given function to differentiate is $ s(t) = t^3 - 2t + 4 $

2Step 2: Apply the power rule of differentiation for each term

The power rule states that the derivative of a function in the form of $ t^n $ is $ n*t^(n-1) $. So, taking derivative of each term, the derivative of $ t^3 $ is $ 3*t^2 $, derivative of $ -2t $ is $ -2 $, and the derivative of constant 4 is zero because the slope of a constant function is zero.

3Step 3: Write the Derivative

Join the derivatives of individual terms to get the derivative of the function. So, the derivative of $ s(t) $ is $ 3*t^2 -2 $.

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