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lovickiy99
@lovickiy99
July 2022
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Найти производную функции
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mikael2
Verified answer
1. y'=2eˣ+6x
y=2log2 x+lnx-2 y'=2/(xln2)+1/x
y=7ˣ+eˣ+cosx y'=7ˣ ln7+eˣ-sinx
2. y=eˣ-x-1 x0=0 y'=eˣ-1 k=y'(0)=e⁰-1=0
3. g(x)=x²*e^(-x²) g'(x)=2xe^(-x²)+x²*e^(-x²)*(-2x)
g'(x)=e^(-x²)[2x-2x³]=0
2x(1-x²)=0 x=0 x=-1 x=1
---------- -1------------ 0--------- 1---------
+ - + -
g(1)=1/e g(-1)=1/e max 1/e
4.F(x)=∫(1/x+3x²)dx=ln|x|+x³+C B(1;3)
ln1+1+C=3 0+1+C=3 C=2
ln|x|+x³+2
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Answers & Comments
Verified answer
1. y'=2eˣ+6xy=2log2 x+lnx-2 y'=2/(xln2)+1/x
y=7ˣ+eˣ+cosx y'=7ˣ ln7+eˣ-sinx
2. y=eˣ-x-1 x0=0 y'=eˣ-1 k=y'(0)=e⁰-1=0
3. g(x)=x²*e^(-x²) g'(x)=2xe^(-x²)+x²*e^(-x²)*(-2x)
g'(x)=e^(-x²)[2x-2x³]=0
2x(1-x²)=0 x=0 x=-1 x=1
---------- -1------------ 0--------- 1---------
+ - + -
g(1)=1/e g(-1)=1/e max 1/e
4.F(x)=∫(1/x+3x²)dx=ln|x|+x³+C B(1;3)
ln1+1+C=3 0+1+C=3 C=2
ln|x|+x³+2