Chain Rule Error In Differentiation

Question

Experimental Procedure: In a physics experiment on oscillatory motion, a student records the displacement of a spring-mass system over time. The displacement is modeled by $$x(t)=3*\sin(2*t+\pi/4)$$. The student attempts to calculate the velocity at t = 1 second by differentiating the displacement function but forgets to account for the derivative of the inner function. What is the mistake in the student’s derivative calculation?

Accepted Answer

The student failed to apply the chain rule by omitting the multiplication by the derivative of the inner function; the correct derivative should be $$x'(t)=3*2*\cos(2*t+\pi/4)$$.

Answer

The error is due to computing the derivative at the wrong time value; the student should have calculated it at t = 0.

Answer

The student incorrectly assumed that the amplitude of the sine function would not affect the velocity calculation.

Answer

The student used the wrong trigonometric function in the derivative, mistakenly using sine instead of cosine.