Question

What are the derivatives of common functions?

Answer 1

1. Constant Rule: \(\frac{d}{d x}(c)=0\), where \(c\) is a constant.
2. Power Rule: \(\frac{d}{d x}\left(x^n\right)=n x^{n-1}\), where \(n\) is an integer, \(n>0\).

3. \(\frac{d}{d x}(\sin x)=\cos x\)
4. \(\frac{d}{d x}(\cos x)=-\sin x\)
5. \(\frac{d}{d x}\left(e^x\right)=e^x\)
6. \(\frac{d}{d x}(\ln x)=\frac{1}{x}\)