Notes for Math 220, Calculus 2

\begin{align*} \frac{d}{dx}x^a \amp= \hspace{5cm} \frac{d}{dx}\sqrt{x} =\\ \frac{d}{dx}\sin x \amp= \hspace{5cm} \frac{d}{dx}\cos x =\\ \frac{d}{dx}\tan x \amp= \hspace{5cm} \frac{d}{dx}\sec x =\\ (\dagger)\frac{d}{dx}\cot x \amp= \hspace{5cm} (\dagger)\frac{d}{dx}\csc x =\\ \frac{d}{dx}e^x \amp= \hspace{5cm} \text{For }a > 0,\; \frac{d}{dx}a^x =\\ \text{For } x>0,\, \frac{d}{dx}\ln x \amp= \hspace{5cm} \text{For } x \neq 0,\, \frac{d}{dx}\ln |x| =\\ \frac{d}{dx}\arcsin x = \frac{d}{dx}\sin^{-1} x \amp= \hspace{5cm} \frac{d}{dx}\arccos x = \frac{d}{dx}\cos^{-1} x =\\ \frac{d}{dx}\tan^{-1} x \amp= \hspace{5cm} \frac{d}{dx}\sec^{-1} x =\\ (\dagger) \frac{d}{dx}\cot^{-1} x \amp= \hspace{5cm} (\dagger) \frac{d}{dx}\csc^{-1} x =\\ \frac{d}{dx}\sinh \amp= \hspace{5cm} \frac{d}{dx}\cosh x =\\ \frac{d}{dx}\tanh \amp= \hspace{5cm} \frac{d}{dx}\sech\ x =\\ (\dagger) \frac{d}{dx}\coth \amp= \hspace{5cm} (\dagger) \frac{d}{dx}\csch\ x =\\ \frac{d}{dx}\sinh^{-1} x \amp= \hspace{5cm} \frac{d}{dx}\cosh^{-1} x =\\ \frac{d}{dx}\tanh^{-1} x \amp= \hspace{5cm} \frac{d}{dx}\sech^{-1} x =\\ (\dagger) \frac{d}{dx}\coth^{-1} x \amp= \hspace{5cm} (\dagger) \frac{d}{dx}\csch^{-1} x = \end{align*}