חשבון אינפיניטסימלי/נגזרת/נגזרות של פונקציות אלנמטריות: הבדלים בין גרסאות בדף

:<math>\frac{d \over }{dx} c = 0</math>

:<math>\frac{d \over }{dx} x = 1</math>

:<math>\frac{d \over }{dx} x^c = cx^{c-1}</math> (כאשר הביטויים <math>\ x^c</math> ו- <math>\ cx^{c-1}</math> מוגדרים)

:<math>\frac{d \over }{dx} e^x = e^x</math>

:<math>\frac{d \over }{dx} a^x = \ln a^x \cdot \ln(a^x)</math>

:<math>\frac{d \over }{dx} \ln (x) = \frac{1 \over }{x} \qquad x > 0</math>

:<math>\frac{d \over }{dx} \log_a (x) = \frac{1}{x \overcdot \ln (a \cdot x)} \qquad x > 0</math>

:<math>\frac{d \over }{dx} \sin (x) = \cos (x)</math>

:<math>\frac{d \over }{dx} \cos (x) = -\sin (x)</math>

:<math>\frac{d \over }{dx} \tan (x) = \sec^2 (x) = \frac{ 1 \over }{\cos^2 (x)}</math>

:<math>\frac{d \over }{dx} \sec (x) = \tan (x) \cdot \sec (x)</math>

:<math>\frac{d \over }{dx} \cot (x) = -\csc^2 (x) = -\frac{ 1 \over }{\sin^2 (x)}</math>

:<math>\frac{d \over }{dx} \csc (x) = -\csc (x) \cdot \cot (x)</math>

:<math>\frac{d \over }{dx} \arcsin (x) = \frac{ 1 \over }{\sqrt{1 - x^2}}</math>

:<math>\frac{d \over }{dx} \arccos (x) = -\frac{ 1 \over }{\sqrt{1 - x^2}}</math>

:<math>\frac{d \over }{dx} \arctan (x) = \frac{ 1 \over 1 + }{x^2+1}</math>

:<math>\frac{d \over }{dx} \arcsec (x) = \frac{ 1 \over }{|x|\sqrt{x^2 - 1}}</math>

:<math>\frac{d \over }{dx} \arccot (x) = -\frac{1 \over 1 + }{x^2+1}</math>

:<math>\frac{d \over }{dx} \arccsc (x) = -\frac{1 \over }{|x|\sqrt{x^2 - 1}}</math>

:<math>\frac{d \over }{dx} \sinh (x) = \cosh (x) = \frac{e^x + e^{-x}}{2}</math>

:<math>\frac{d \over }{dx} \cosh (x) = \sinh (x) = \frac{e^x - e^{-x}}{2}</math>

:<math>\frac{d \over }{dx} \tanh (x) = \operatorname{sech}^2\,(x)</math>

:<math>\frac{d \over }{dx}\,\operatorname{sech}\,(x) = - \tanh(x) x\,cdot \operatorname{sech}\,(x)</math>

:<math>\frac{d \over }{dx}\,\operatorname{coth}\,(x) = -\,\operatorname{csch}^2\,(x)</math>

:<math>\frac{d \over }{dx}\,\operatorname{csch}\,x = -\,\operatorname{coth}\,(x) \,cdot \operatorname{csch}\,(x)</math>

:<math>\frac{d \over }{dx}\,\operatorname{arcsinharsinh}\,(x) = \frac{ 1 \over }{\sqrt{x^2 + 1}}</math>

:<math>\frac{d \over }{dx}\,\operatorname{arccosharcosh}\,(x) = \frac{ 1 \over }{\sqrt{x^2 - 1}}</math>

:<math>\frac{d \over }{dx}\,\operatorname{arctanhartanh}\,(x) = \frac{ 1 \over }{1 - x^2}</math>

:<math>\frac{d \over }{dx}\,\operatorname{arcsecharsech}\,(x) = -\frac{ 1 \over }{x\sqrt{1 - x^2}}</math>

:<math>\frac{d \over }{dx}\,\operatorname{arccotharcoth}\,(x) = \frac{ 1 \over }{1 - x^2}</math>

:<math>\frac{d \over }{dx}\,\operatorname{arccscharcsch}\,(x) = -\frac{1 \over }{|x|\sqrt{1 + x^2+1}}</math>