Math  /  Calculus

Question2. (1,0 ponto cada item) Usando as regras de diferenciaçāo, encontre as derivadas das funçöes a seguir, simplificando ao máximo se possível. (a) y=senxcosx1y=\frac{\operatorname{sen} x}{\cos x-1} (c) y=cos(2x)y=\cos \left(2^{x}\right) (b) f(x)=xarctgx12ln(1+x2)f(x)=x \operatorname{arctg} x-\frac{1}{2} \ln \left(1+x^{2}\right) (d) y=(x)(coshx)y=(x)^{(\cosh x)}

Studdy Solution
(a) 11cosx\frac{1}{1 - \cos x} (b) arctgx\operatorname{arctg} x (c) 2xln2sen(2x)-2^x \ln 2 \operatorname{sen}(2^x) (d) xcoshx(senhxlnx+coshxx)x^{\cosh x}\left(\operatorname{senh} x \ln x + \frac{\cosh x}{x}\right)

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