Title: The Chain Rule Post-Video Questions
Course: Calculus Videos Project > Section: The Chain Rule

Q: f(x) = ln(sin(x)), f'(x) =
- \(\frac{1}{\sin\left(x\right)}\)
- \(\tan\left(x\right)\)
- \(\frac{\cos\left(x\right)}{\sin\left(x\right)}\)
- \(\frac{\cos\left(x\right)}{x}\)
- \(\tan^{-1}\left(x\right)\)
A: \(\frac{\cos\left(x\right)}{\sin\left(x\right)}\)

Q: f(x) = 3^sin(x), f'(x) =
- \(3^{\cos\left(x\right)}\)
- \(3^{\sin\left(x\right)}·\:\ln\left(3\right)\:·\:\cos\left(x\right)\)
- \(3^{\sin\left(x\right)}\:·\:\cos\left(x\right)\)
- \(3^{\cos\left(x\right)}\:·\:\ln\left(3\right)\)
- \(\sin\left(x\right)\:·\:3^{\sin\left(x\right)-1}\)
A: \(3^{\sin\left(x\right)}·\:\ln\left(3\right)\:·\:\cos\left(x\right)\)

Q: f(x) = cos(6x^3-4), f'(x) =
- \(-\sin\left(18x^2\right)\)
- \(\cos\left(18x^2\right)\:·\:\left(-\sin\left(x\right)\right)\)
- \(-\sin\left(x\right)\:·\:18x^2\)
- \(\cos\left(6x^3-4\right)\:·\:18x^2\)
- \(-\sin\left(6x^3-4\right)\:·\:18x^2\)
A: \(-\sin\left(6x^3-4\right)\:·\:18x^2\)