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edw213
@edw213
July 2022
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наидите производную функции 1)y=x^4/lnx 2)y=(2x^4-x^3)*(2x^2+3x+4) 3)y=ctg5x 5 баллов за каждое задание заранее спасибо
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sangers1959
Verified answer
Y=x⁴/lnx
y`=(4x³*lnx-x⁴*1/x)/ln²x=x³(4lnx-1)/ln²x.
y=(2x⁴-x³)*(2x²+3x+4)
y`=(8x³-3x²)*(2x²+3x+4)+(2x⁴-x³)*(4x+3)=
=x²*(8x-3)*(2x²+3x+4)+x³*(2x+3)*(4x+3)=x²((8x-3)(2x²+3x+4)+(2x²+3x)(4x+3)).
y=ctg(5x)=cos(5x)/sin(5x)
y`=(-5sin(5x)*sin(5x)-cos(5x)*5cos(5x))/sin²(5x)=
=-5(sin²(5x)+cos²(5x)/sin²(5x)=-5/sin²(5x)=-5csc²(5x).
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Answers & Comments
Verified answer
Y=x⁴/lnxy`=(4x³*lnx-x⁴*1/x)/ln²x=x³(4lnx-1)/ln²x.
y=(2x⁴-x³)*(2x²+3x+4)
y`=(8x³-3x²)*(2x²+3x+4)+(2x⁴-x³)*(4x+3)=
=x²*(8x-3)*(2x²+3x+4)+x³*(2x+3)*(4x+3)=x²((8x-3)(2x²+3x+4)+(2x²+3x)(4x+3)).
y=ctg(5x)=cos(5x)/sin(5x)
y`=(-5sin(5x)*sin(5x)-cos(5x)*5cos(5x))/sin²(5x)=
=-5(sin²(5x)+cos²(5x)/sin²(5x)=-5/sin²(5x)=-5csc²(5x).