Resposta:
a) eˣ + 1/x + cos(x) + 6x
b) sec²(x) + 1/xln(3) + 5ˣln(5) - 7/x⁸
Explicação passo-a-passo:
a)
[tex]\frac{d}{dx}\left(e^x+\ln \left(x\right)+\sin \left(x\right)+3x^2\right)\\=\frac{d}{dx}\left(e^x\right)+\frac{d}{dx}\left(\ln \left(x\right)\right)+\frac{d}{dx}\left(\sin \left(x\right)\right)+\frac{d}{dx}\left(3x^2\right)\\=e^x+\frac{1}{x}+\cos \left(x\right)+6x[/tex]
b)
[tex]\frac{d}{dx}\left(\tan \left(x\right)+\log _3\left(x\right)+5^x+\frac{1}{x^7}\right)\\=\frac{d}{dx}\left(\tan \left(x\right)\right)+\frac{d}{dx}\left(\log _3\left(x\right)\right)+\frac{d}{dx}\left(5^x\right)+\frac{d}{dx}\left(\frac{1}{x^7}\right)\\=\sec ^2\left(x\right)+\frac{1}{x\ln \left(3\right)}+5^x\ln \left(5\right)-\frac{7}{x^8}[/tex]
