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diff --git a/spec/calculus.md b/spec/calculus.md
index 4c3331860356d8310bfdf56c7fb075fbc790b0dc..19f97b5aba2cf5b39bcd3ac26dba6f801a4bdc49 100644 (file)
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -93,7 +93,7 @@ where $u$ and $v$ are functions of $x$
 
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
 
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 

-## Chain rule
+## Chain rule for $(f\circ g)$

 
 $$(f \circ g)^\prime = (f^\prime \circ g) \cdot g^\prime$$
 
 
 $$(f \circ g)^\prime = (f^\prime \circ g) \cdot g^\prime$$
 


@@ -130,3 +130,16 @@ If $f(x)={u(x) \over v(x)}$, then $f^\prime(x)={{v(x)u^\prime(x)-u(x)v^\prime(x)
 
 If $y={u(x) \over v(x)}$, then derivative ${dy \over dx} = {{v{du \over dx} - u{dv \over dx}} \over v^2}$
 
 
 If $y={u(x) \over v(x)}$, then derivative ${dy \over dx} = {{v{du \over dx} - u{dv \over dx}} \over v^2}$
 

+## Solving $e^x$
+
+| $f(x)$ | $f^\prime(x)$ |
+| ------ | ------------- |
+| $\sin x$ | $\cos x$ |
+| $\sin ax$ | $a\cos ax$ |
+| $\cos x$ | $-\sin x$ |
+| $\cos ax$ | $-a \sin ax$ |
+| $e^x$ | $e^x$ |
+| $e^{ax}$ | $ae^{ax}$ |
+| $\log_e x$ | $1 \over x$ |
+| $\log_e {ax}$ | $1 \over x$ |
+