| $\sin ax$ | $a\cos ax$ |
| $\cos x$ | $-\sin x$ |
| $\cos ax$ | $-a \sin ax$ |
+| $\tan f(x)$ | $f^2(x) \sec^2f(x)$ |
| $e^x$ | $e^x$ |
| $e^{ax}$ | $ae^{ax}$ |
| $ax^{nx}$ | $an \cdot e^{nx}$ |
| $\log_e {ax}$ | $1 \over x$ |
| $\log_e f(x)$ | $f^\prime (x) \over f(x)$ |
| $\sin(f(x))$ | $f^\prime(x) \cdot \cos(f(x))$ |
+| $\sin^{-1} x$ | $1 \over {\sqrt{1-x^2}}$ |
+| $\cos^{-1} x$ | $-1 \over {sqrt{1-x^2}}$ |
+| $\tan^{-1} x$ | $1 \over {1 + x^2}$ |
<!-- $${d(ax^{nx}) \over dx} = an \cdot e^nx$$ -->
+Reciprocal derivatives:
+
+$${{dy \over dx} \over 1} = dx \over dy$$
+
+## Differentiating $x=f(y)$
+
+Find $dx \over dy$. Then $dx \over dy = {1 \over {dy \over dx}} \therefore {dy \over dx} = {1 \over {dx \over dy}$
+
## Antidifferentiation
$$y={x^{n+1} \over n+1} + c$$
To find stationary points of a function, substitute $x$ value of given point into derivative. Solve for ${dy \over dx}=0$. Integrate to find original function.
-## Kinematics
-
-$${dV \over dt} = {\operatorname{change in volume} \over \operatorname{respect to time}}$$
-
-` |->--diff-->--| |-->--diff-->--|
-displacement velocity acceleration
- |--<-antidiff-<---| |--<-antidiff-<-|`
-
-**displacement $x$** - change in position
-**velocity $v$** - change in displacement
-**acceleration $a$** - change in velocity
-
-$$v_{\operatorname{avg}}={\Delta x \over \Delta t}={{x_2 - x_1} \over {t_2 - t_1}}$$
-$$\operatorname{speed}_{\operatorname{avg}}={\Delta v \over \Delta t}$$
-