Easy derivative but it took me 30 minutes! @blackpenredpen

Uploaded November 2023 | Updated September 2026, 2 weeks ago

We will find the second derivative of sin(x^2) but with a limit definition that you probably haven't seen before! This took me 32 minutes!

0:00 finding the second derivative of sin(x^2) but no differentiation shortcuts
0:54 Definition of derivative, symmetric derivative, and second symmetric derivative in terms of limits
7:46 The real action!!
9:08 The formula for sin(A)+sin(B)
12:01 Back to the limit
29:50 Check the answer!

Check out my 100-limit video for more calculus limit practice. youtu.be/TglD4Y6lmQk?si=lR_jfa-gI8FVO7VS
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