Início/Cálculo diferencial/Apêndice A: tabela extensa de derivadas/A.5 Composições frequentesConteúdoA.5 Composições frequentesFórmulaCopiar LaTeXddx(sen(g(x)))=cos(g(x))⋅g′(x)\frac{d}{dx}(\operatorname{sen}(g(x)))=\cos(g(x))\cdot g'(x)dxd(sen(g(x)))=cos(g(x))⋅g′(x)Ver detalhe →FórmulaCopiar LaTeXddx(cos(g(x)))=−sen(g(x))⋅g′(x)\frac{d}{dx}(\cos(g(x)))=-\operatorname{sen}(g(x))\cdot g'(x)dxd(cos(g(x)))=−sen(g(x))⋅g′(x)Ver detalhe →FórmulaCopiar LaTeXddx(eg(x))=eg(x)g′(x)\frac{d}{dx}(e^{g(x)})=e^{g(x)}g'(x)dxd(eg(x))=eg(x)g′(x)Ver detalhe →FórmulaCopiar LaTeXddx[ln(g(x))]=g′(x)g(x),g(x)>0\frac{d}{dx}[\ln(g(x))]=\frac{g'(x)}{g(x)},\qquad g(x)>0dxd[ln(g(x))]=g(x)g′(x),g(x)>0g(x)>0g(x)>0g(x)>0Ver detalhe →FórmulaCopiar LaTeXddx((g(x))n)=n(g(x))n−1g′(x),n∈Z, g(x)≠0 se n<0\frac{d}{dx}((g(x))^n)=n(g(x))^{n-1}g'(x),\qquad n\in\mathbb{Z},\ g(x)\neq 0\ \text{se }n<0dxd((g(x))n)=n(g(x))n−1g′(x),n∈Z, g(x)=0 se n<0n∈Z, g(x)≠0 se n<0n\in\mathbb{Z},\ g(x)\neq 0\ \text{se }n<0n∈Z, g(x)=0 se n<0Ver detalhe →FórmulaCopiar LaTeXddx(arctan(g(x)))=g′(x)1+(g(x))2\frac{d}{dx}(\arctan(g(x)))=\frac{g'(x)}{1+(g(x))^2}dxd(arctan(g(x)))=1+(g(x))2g′(x)Ver detalhe →FórmulaCopiar LaTeXddx[arcsen(g(x))]=g′(x)1−(g(x))2,∣g(x)∣<1\frac{d}{dx}[\operatorname{arcsen}(g(x))]=\frac{g'(x)}{\sqrt{1-(g(x))^2}},\qquad |g(x)|<1dxd[arcsen(g(x))]=1−(g(x))2g′(x),∣g(x)∣<1∣g(x)∣<1|g(x)|<1∣g(x)∣<1Ver detalhe →*Gerado com 161 fórmulas catalogadas (DIF-001 … DIF-161).
FórmulaCopiar LaTeXddx(sen(g(x)))=cos(g(x))⋅g′(x)\frac{d}{dx}(\operatorname{sen}(g(x)))=\cos(g(x))\cdot g'(x)dxd(sen(g(x)))=cos(g(x))⋅g′(x)Ver detalhe →
FórmulaCopiar LaTeXddx(cos(g(x)))=−sen(g(x))⋅g′(x)\frac{d}{dx}(\cos(g(x)))=-\operatorname{sen}(g(x))\cdot g'(x)dxd(cos(g(x)))=−sen(g(x))⋅g′(x)Ver detalhe →
FórmulaCopiar LaTeXddx(eg(x))=eg(x)g′(x)\frac{d}{dx}(e^{g(x)})=e^{g(x)}g'(x)dxd(eg(x))=eg(x)g′(x)Ver detalhe →
FórmulaCopiar LaTeXddx[ln(g(x))]=g′(x)g(x),g(x)>0\frac{d}{dx}[\ln(g(x))]=\frac{g'(x)}{g(x)},\qquad g(x)>0dxd[ln(g(x))]=g(x)g′(x),g(x)>0g(x)>0g(x)>0g(x)>0Ver detalhe →
FórmulaCopiar LaTeXddx((g(x))n)=n(g(x))n−1g′(x),n∈Z, g(x)≠0 se n<0\frac{d}{dx}((g(x))^n)=n(g(x))^{n-1}g'(x),\qquad n\in\mathbb{Z},\ g(x)\neq 0\ \text{se }n<0dxd((g(x))n)=n(g(x))n−1g′(x),n∈Z, g(x)=0 se n<0n∈Z, g(x)≠0 se n<0n\in\mathbb{Z},\ g(x)\neq 0\ \text{se }n<0n∈Z, g(x)=0 se n<0Ver detalhe →
FórmulaCopiar LaTeXddx(arctan(g(x)))=g′(x)1+(g(x))2\frac{d}{dx}(\arctan(g(x)))=\frac{g'(x)}{1+(g(x))^2}dxd(arctan(g(x)))=1+(g(x))2g′(x)Ver detalhe →
FórmulaCopiar LaTeXddx[arcsen(g(x))]=g′(x)1−(g(x))2,∣g(x)∣<1\frac{d}{dx}[\operatorname{arcsen}(g(x))]=\frac{g'(x)}{\sqrt{1-(g(x))^2}},\qquad |g(x)|<1dxd[arcsen(g(x))]=1−(g(x))2g′(x),∣g(x)∣<1∣g(x)∣<1|g(x)|<1∣g(x)∣<1Ver detalhe →