导数

1. 一般求导法则

$$ \frac{\mathrm{d}a f(x)}{\mathrm{d} x} = a \frac{\mathrm{d} f(x)}{\mathrm{d} x} $$ $$ h'(x) = \frac{f(x)}{g(x)} = \frac{f'(x)g(x) - f(x)g'(x)}{g^2(x)} $$

2. 指数、对数函数的导

$$ \frac{\mathrm{d} e^x}{\mathrm{d} x} = e^x $$ $$ \frac{\mathrm{d} a^x}{\mathrm{d} x} = a^x \ln a $$

3. 三角函数的导

$$ \sin'(x) = \cos (x) $$ $$ \cos'(x) = -\sin (x) $$