A student tries to differentiate p(x)=7x3−4cosx+5 and writes the following result:
p′(x)=21x2−4sinx+5.
Study the work and answer the following:
a. (i) Copy the student’s derivative and identify the specific term(s) where an error has been made. Give a brief explanation of the mistake.
b. (ii) Determine the correct derivative p′(x).
c. (iii) Verify your result by evaluating the correct derivative at x=3π. Give the exact value.