$$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
**Tangent line** of function $f$ at point $M(a, f(a))$ is the line through $M$ with gradient $f^\prime(a)$.
+
+## Tangents and gradients
+
+
+### Tangent of a point
+
+For a point $P(q,r)$ on function $f$, the gradient of the tangent is the derivative $dy \over dx$ of $f(q)$. Therefore the tangent line is defined by $y=mx+c$ where $m={dy \over dx}$. Substitute $x=q, \hspace{0.5em} y=q$ to solve for $c$.
+
+### Normal
+
+Normal $\perp$ tangent.
+
+$$m_{\operatorname{tan}} \cdot m_{\operatorname{norm}} = -1$$
+
+Normal line for point $P(q,r)$ on function $f$ is $y=mx+c$ where $m={-1 \over m_{\tan}}$. To find $c$, substitute $(x, y)=(q,r)$ and solve.
+
+### Solving on CAS
+
+**In main**: type function. Interactive -> Calculation -> Line -> (Normal | Tan line)
+**In graph**: define function. Analysis -> Sketch -> (Normal | Tan line). Type $x$ value to solve for a point. Return to show equation for line.
--- /dev/null
+# Light and matter
+
+## Photoelectric effect
+
+### Planck's equation
+
+$$E=hf$$
+
+where
+$E$ is energy of a quantum of light (J)
+$f$ is frequency of EM radiation
+$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}$)
+
+
+### Electron diffraction patterns
+
+$$W=qV$$
+
+(work for accelerating electon of charge $q$ with voltage $V$)
+
+$$\lambda = {h \over mv}$$
+
+(de Broglie's equation)
+
+Solving wavelength of electrons from gun:
+1.
+
+774 abc melbourne
\ No newline at end of file
$$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
-## Chain rule
+## Chain rule for $(f\circ g)$
$$(f \circ g)^\prime = (f^\prime \circ g) \cdot g^\prime$$
### Differentiating logarithms
$${d \over dx} \log_b x = {1 \over x \ln b}$$
+## Solving $e^x$
+
+| $f(x)$ | $f^\prime(x)$ |
+| ------ | ------------- |
+| $\sin x$ | $\cos x$ |
+| $\sin ax$ | $a\cos ax$ |
+| $\cos x$ | $-\sin x$ |
+| $\cos ax$ | $-a \sin ax$ |
+| $e^x$ | $e^x$ |
+| $e^{ax}$ | $ae^{ax}$ |
+| $\log_e x$ | $1 \over x$ |
+| $\log_e {ax}$ | $1 \over x$ |