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• Математика

• $\dfrac{d}{d x} c=0$
• $\dfrac{d}{d x} x=1$
• $\dfrac{d}{d x} c x=c$
• $\dfrac{d}{d x} x^{c}=c x^{c-1}$
• $\dfrac{d}{d x}\left(\dfrac{1}{x}\right)=\dfrac{d}{d x}\left(x^{-1}\right)=-x^{-2}=-\dfrac{1}{x^{2}}$
• $\dfrac{d}{d x}\left(\dfrac{1}{x^{c}}\right)=\dfrac{d}{d x}\left(x^{-c}\right)=-\dfrac{c}{x^{c+1}}$
• $\dfrac{d}{d x} \sqrt{x}=\dfrac{d}{d x} x^{\dfrac{1}{2}}=\dfrac{1}{2} x^{-\dfrac{1}{2}}=\dfrac{1}{2 \sqrt{x}}, \quad x>0$
• $\dfrac{d}{d x} \sqrt[n]{x}=\dfrac{d}{d x} x^{\dfrac{1}{n}}=\dfrac{1}{n} x^{\dfrac{1-n}{n}}=\dfrac{1}{n \cdot \sqrt[n]{x^{n-1}}}$

• $\dfrac{d}{d x} c^{x}=c^{x}lnx$
• $\dfrac{d}{d x} e^{x}=e^{x}$
• $\dfrac{d}{d x} e^{f(x)}=f^{\prime}(x) e^{f(x)}$
• $\dfrac{d}{d x} \ln x=\dfrac{1}{x}$
• $\dfrac{d}{d x} \log _{a} x=\dfrac{\log _{a} e}{x}=\dfrac{1}{x \ln a}$

• $\dfrac{d}{d x} \cos x=-\sin x$
• $\dfrac{d}{d x} \sin x=\cos x$
• $\dfrac{d}{d x} \operatorname{tg} x=\sec ^{2} x=\dfrac{1}{\cos ^{2} x}=\operatorname{tg}^{2} x+1$
• $\dfrac{d}{d x} \operatorname{ctg} x=-\operatorname{cosec}^{2} x=-\dfrac{1}{\sin ^{2} x}$
• $\dfrac{d}{d x} \sec x=\operatorname{tg} x \sec x$
• $\dfrac{d}{d x} \operatorname{cosec} x=-\operatorname{ctg} x \operatorname{cosec} x$
• $\dfrac{d}{d x} \arcsin x = \dfrac{1}{\sqrt{1-x^{2}}}$
• $\dfrac{d}{d x} \arccos x =-\dfrac{1}{\sqrt{1-x^{2}}}$
• $\dfrac{d}{d x} \operatorname{arctg} x =\dfrac{1}{1+x^{2}}$
• $\dfrac{d}{d x} \operatorname{arcctg} x =-\dfrac{1}{1+x^{2}}$
• $\dfrac{d}{d x} \operatorname{arcsec} x =\dfrac{1}{|x| \sqrt{x^{2}-1}}$
• $\dfrac{d}{d x} \operatorname{arccosec} x =-\dfrac{1}{|x| \sqrt{x^{2}-1}}$

• @TablicaProizvodnyh2022