微分

導関数の四則演算について示す．

$f\left(x\right)=g\left(x\right)+h\left(x\right)$のとき $f'\left(x\right)=g'\left(x\right)+h'\left(x\right)$.

$f\left(x\right)=g\left(x\right)-h\left(x\right)$のとき $f'\left(x\right)=g'\left(x\right)-h'\left(x\right)$.

$f\left(x\right)=g\left(x\right)h\left(x\right)$のとき $f'\left(x\right)=g'\left(x\right)h\left(x\right)+g\left(x\right)h'\left(x\right)$.

$f\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)}$のとき $f'\left(x\right)=\frac{g'\left(x\right)}{h\left(x\right)}-\frac{g\left(x\right)h'\left(x\right)}{h\left(x\right)^2}$.

$a$を定数として$f\left(x\right)=ag\left(x\right)$のとき$f'\left(x\right)=ag'\left(x\right)$.