Using derivative rules, please find the derivatives of the following functions. In some cases, you may...

       

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Using derivative rules, please find the derivatives of the following functions. In some cases, you may need to simplify or expand first given derivative rules covered so far. a) f(x)=e b) g(t) = 3t+1 Final Answer Final Answer c) f(x)=x7 Final Answer Q#4 A hockey player skates from the red to the blue line (8 meters) in 4 seconds crossing the blue line at 5 meters per second. Given that velocity (speed) represents the rate of change of position, please do the following: a) Find an average velocity in meters per sec.) in this situation. b) Find an instantaneous velocities (in meters per sec.) in this situation. Final Answer Final Answer c) State whether (a) or (b) is given by the derivative. Final Answer (enter a or b) Using the definition of the derivative function*. please prove the Constant Multiple Rule, namely that (cf (x))' = cf'(x). f'(x)=Lim f(x+h)-f(x) h0 h Using derivative rules, please find the derivatives of the following functions. In some cases, you may need to simplify or expand first given derivative rules covered so far. a) f(x)=e b) g(t) = 3t+1 Final Answer Final Answer c) f(x)=x7 Final Answer Q#4 A hockey player skates from the red to the blue line (8 meters) in 4 seconds crossing the blue line at 5 meters per second. Given that velocity (speed) represents the rate of change of position, please do the following: a) Find an average velocity in meters per sec.) in this situation. b) Find an instantaneous velocities (in meters per sec.) in this situation. Final Answer Final Answer c) State whether (a) or (b) is given by the derivative. Final Answer (enter a or b) Using the definition of the derivative function*. please prove the Constant Multiple Rule, namely that (cf (x))' = cf'(x). f'(x)=Lim f(x+h)-f(x) h0 h