f(t) dt = f(x). We get dt = 3 = 27x^2 − 9x. Don’t forget
that because the upper limit is a function, we need to multiply the answer by the derivative of
that function.
- −2 cos x
We find the derivative of an integral using the Second Fundamental Theorem of Calculus:
f(t) dt = f(x). We get −2 cos t dt = −2 cos x.
SOLUTIONS TO PRACTICE PROBLEM SET 22
1.
We find the derivative of the inverse tangent using the formula (tan−1 u) = . Here
we have u = , so = . Therefore, = =
.
2.
We find the derivative of the inverse sine using the formula (sin−1 u) = . Here
we have u = , so . Therefore, = =
= .
