What’s the difference between differential and inferential Calculus? And How do they apply to physics?

Can I get an easy explanation

a) If a company spends r million dollars on research, it sales will be s million dollars, where r and s are related by s2 = r3 − 60. ds/dr= ________ Interpret your answer to part (a) as a rate of change. b) Find dr/ds by implicit differentiation and evaluate it at r = 4, s = 2. [Hint: Differentiate the original equation with respect to s.] dr/ds=___________ Interpret your answer to part (b) as a rate of change.

In the previous Problem Set question, we started looking at the position functions (t), the position of an object at time t. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time is as (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time his (s(t+h)-s(t)) If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h→0. i.e. the derivative a' (t). Use this function in the model below for the velocity function (). h The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t) = ✔ (t) =" (t). Problem set question: A particle moves according to the position functions (t) = etsin (2). Enclose arguments of functions in parentheses. For example, sin…

Please answer the question providing all steps and clear writing so I can understand. Thanks.   You can see as a Reference book "James Stewart Calculus 8th Edition" so you can see similar solutions.