вычислите производные функций y=f(x) зодание в вложениях

Question

вычислите производные функций y=f(x)

зодание в вложениях

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Answer 1

a). f(x) = cos(x-π/6)

f ' (x) = (cos(x-π/6)) ' = -sin(x-π/6)*(x-π/6) ' = -sin(x-π/6)*1 = -sin(x-π/6)

 

б). f(x) = sin(π/4 -x)

f '(x) = cos(π/4 -x)*(π/4 -x) ' = cos(π/4 -x)*(-1) = - cos(π/4 -x)

 

в). f(x)=ctg(π/6 +x)

f '(x) = -(1/sin²(π/6 + x))*(π/6 +x) ' = -(1/sin²(π/6 + x))*1 = -(1/sin²(π/6 + x))

 

г). f(x) = tg(x+π/3)

f '(x) = 1/cos²(x+π/3)*(x+π/3) ' = 1/cos²(x+π/3)*1 = 1/cos²(x+π/3)

Answer 2

1) -sin(x-pi/6)

2) -cos(pi/4-x)

3)-1/siin^2(pi/6+x)

4)1/cos^2(x+pi/3)