From 3f65163e1778a275fb547ee91d2930652e5af85a Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Sat, 18 Aug 2018 16:52:23 +1000 Subject: [PATCH] logs etc --- spec/calculus.md | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/spec/calculus.md b/spec/calculus.md index 4c33318..19f97b5 100644 --- 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 $(f\circ g)$ $$(f \circ g)^\prime = (f^\prime \circ g) \cdot g^\prime$$ @@ -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 ${dy \over dx} = {{v{du \over dx} - u{dv \over dx}} \over v^2}$ +## Solving $e^x$ + +| $f(x)$ | $f^\prime(x)$ | +| ------ | ------------- | +| $\sin x$ | $\cos x$ | +| $\sin ax$ | $a\cos ax$ | +| $\cos x$ | $-\sin x$ | +| $\cos ax$ | $-a \sin ax$ | +| $e^x$ | $e^x$ | +| $e^{ax}$ | $ae^{ax}$ | +| $\log_e x$ | $1 \over x$ | +| $\log_e {ax}$ | $1 \over x$ | + -- 2.49.0