\(y=\left(x^7+x\right)^3\)

\(y'=3\left(x^7+x\right)^2.\left(x^7+x\right)'=3\left(x^7+x\right)^2\left(7x^6+1\right)\)

\(=8\cdot25-72:9=200-8=192\)

= 8 . 25 - 72 : 9

= 200 - 8

= 192

2^3.25-72:3^2

=8.25-72:9

=192

Câu 11.

a)Độ tự cảm của ống dây:

\(L=4\pi\cdot10^{-7}\cdot\dfrac{N^2}{l}S=4\pi\cdot10^{-7}\cdot\dfrac{1000^2}{0,2}\cdot50\cdot10^{-4}=0,0314H=0,0314\cdot10^3=31,4mH\)

b)Độ biến thiên từ thông:

\(\Delta\Phi=L\cdot\Delta i=0,0314\cdot\left(1-0\right)=0,0314Wb\)

Suất điện động cảm ứng:

\(e_{tc}=\left|-\dfrac{\Delta\Phi}{\Delta t}\right|=\left|-\dfrac{0,0314}{0,1}\right|=0,314V\)

ảnh mờ quá bn ơi

7.

\(y'=\left(-x^3\right)'-\left(5x\right)'+\left(2\right)'=-3x^2-5\)

\(y''=\left(-3x^2\right)'-\left(5\right)'=-6x\)

8.

\(\lim\limits_{x\rightarrow+\infty}\left(x^3+3x-2\right)=\lim\limits_{x\rightarrow+\infty}x^3\left(1+\dfrac{3}{x^2}-\dfrac{2}{x^3}\right)\)

Do: \(\lim\limits_{x\rightarrow+\infty}x^3=+\infty\)

\(\lim\limits_{x\rightarrow+\infty}\left(1+\dfrac{3}{x^2}-\dfrac{2}{x^3}\right)=1>0\)

\(\Rightarrow\lim\limits_{x\rightarrow+\infty}x^3\left(1+\dfrac{3}{x^2}-\dfrac{2}{x^3}\right)=+\infty\)

(3x)^2=3^2.x^2=9x^2