№1 (а)
ответ: -\frac{4}{3}" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=x%20%3E%20-%5Cfrac%7B4%7D%7B3%7D" title="x > -\frac{4}{3}">
№1 (б)
№2 (а)
-4} \atop {x\leq -2.5}} \right." class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%3E-4%7D%20%5Catop%20%7Bx%5Cleq%20-2.5%7D%7D%20%5Cright." title="\left \{ {{x>-4} \atop {x\leq -2.5}} \right.">
№2(б)
\frac{36}{5}" class="latex-formula" id="TexFormula10" src="https://tex.z-dn.net/?f=x%20%3E%20%5Cfrac%7B36%7D%7B5%7D" title="x > \frac{36}{5}">
ответ: \frac{36}{5}" class="latex-formula" id="TexFormula12" src="https://tex.z-dn.net/?f=x%20%3E%20%5Cfrac%7B36%7D%7B5%7D" title="x > \frac{36}{5}">
Найдите производную функции
10. y = (1/3)sinx³ ;
12. y = cos³(7x+1) ;
14. y = ( x² -1 )/(2x²+3) .
ответ: 10. x²cosx³ ; 12. - 21cos²(7x+1)*sin(7x+1) ; 14. 10x / (2x²+3)² .
Объяснение:
10.
y ' = ( (1/3)sinx³ ) ' =(1/3)*(sinx³ ) '=(1/3)*(cosx³)*(x³) ' = (1/3)*(cosx³)*3x² =
x²cosx³.
12.
y ' = ( cos³(7x+1) ) ' = 3cos²(7x+1)* ( cos(7x+1) ) ' =
3cos²(7x+1)*( -sin(7x+1 ) *(7x+1) ' = - 3cos²(7x+1)*sin(7x+1 ) *(7*(x)'+1 ') =
- 3cos²(7x+1)*sin(7x+1 )*(7*1+0) = -21cos²(7x+1)sin(7x+1 ) .
14.
y '= ( ( x² -1 )/(2x²+3) ) ' =( (x² -1 )' *(2x²+3) - (x² -1) *(2x²+3) ' ) /(2x²+3)² =
( 2x(2x²+3) - (x² -1) *4x ) /(2x²+3)² = 10x / (2x²+3)².
Подставь (4-3,5)(3,5+1,5)=0,5*5=2,5