Вычислить f ' (0), если f(x) = - (минус перед дробью) (x+1)/(cosx). Created by KimmDara. algebra-ru

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KimmDara @KimmDara

August 2022 2 6 Report

Вычислить f ' (0), если f(x) = - (минус перед дробью) (x+1)/(cosx)

mikael2

Verified answer

Используем (u/v)'=1/v²[u'v-v'u] u=-(x+1) v=cosx

f'=1/cos²x[-1*c0sx+(x+1)(-sinx)]=- (cosx+sinx+xsinx)/cos²x

f'(0)=-1

1 votes Thanks 1

Alexandr130398 $f(x)=- \frac{x+1}{cosx} \\ f'(x)=- \frac{(x+1)'cosx-(cosx)'(x+1)}{cos ^{2} x} = -\frac{cosx+sinx(x+1)}{cos ^{2} x} \\ f'(0)=-\frac{cos0+sin0(0+1)}{cos ^{2} 0}=- \frac{1+0*1}{1^{2} } =-1 \\ OTBET: -1$

2 votes Thanks 2

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