AP Calculus BC / Unit 2: Differentiation: Definition and Fundamental Properties
2.7 Derivatives of cos x, sin x, e^x, and ln x
Notes
- $\displaystyle \frac{d}{dx}\sin x=\cos x$
- $\displaystyle \frac{d}{dx}\cos x=-\sin x$
- $\displaystyle \frac{d}{dx}e^x=e^x$
- $\displaystyle \frac{d}{dx}\ln x=\frac{1}{x}$ for $x>0$
Practice
$\displaystyle \frac{d}{dx}(3\sin x-2\cos x)=$
$-2(-\sin x)=+2\sin x$.
$\displaystyle \frac{d}{dx}(e^x+\ln x)$ at $x=1$ equals:
$\displaystyle e^1+\frac{1}{1}$.
The slope of $y=\cos x$ at $\displaystyle x=\frac{\pi}{2}$ is:
$\displaystyle -\sin\frac{\pi}{2}=-1$.
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