logarithmic derivatives

diff --git a/spec/calculus.md b/spec/calculus.md
index 1f3d404a908eb59d373868cb5710f97b5ac51fe3..2b68bf5692bec02045cdccc1b1d81146c69ecd72 100644 (file)
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -93,7 +93,7 @@ where $u$ and $v$ are functions of $x$
 
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
-## Chain rule
+## Chain rule for $(f\circ g)$
 
 $$(f \circ g)^\prime = (f^\prime \circ g) \cdot g^\prime$$
 
@@ -151,4 +151,16 @@ $$\ln x = \log_e x$$
 ### Differentiating logarithms
 $${d \over dx} \log_b x = {1 \over x \ln b}$$
 
+## Solving $e^x$
+
+| $f(x)$ | $f^\prime(x)$ |
+| ------ | ------------- |
+| $\sin x$ | $\cos x$ |
+| $\sin ax$ | $a\cos ax$ |
+| $\cos x$ | $-\sin x$ |
+| $\cos ax$ | $-a \sin ax$ |
+| $e^x$ | $e^x$ |
+| $e^{ax}$ | $ae^{ax}$ |
+| $\log_e x$ | $1 \over x$ |
+| $\log_e {ax}$ | $1 \over x$ |