Найдите производную функции.Есть вложение.

16) f '(x) = 56(8x +7)^6 17) f '(x) 1/(2√(x^15 +2x^3 +3)) * (15x^14 +6x²) 18) f (x) = 1/Ctgx = tgx f '(x) = 1/Cos²x 19) f '(x) = 5Cos 5x 20) f '(x) = 2Sin(π/3 -2x) 21) f '(x) = 20x + (3x² -2)/(x³ -2x)² 2) f '(x) = -12x^4 +4x f '(-4) = -12* (-4)^4 +4*(-4) = -12*256 -16 = 3088 f '(-1/2) = -12* 1/16 +4*(-1/2) = -3/4 -2 = -2 3/4

16. [latex]f(x)=(8x+6)^7 \\ f'(x)=7(8x+6)^6*8=56(8x+6)^6[/latex] 17. [latex]f(x)= \sqrt{x^{15}+2x^2+3} \\ f'(x)= \frac{1}{ \sqrt{x^{15}+2x^2+3} }*(15x^{14}+4x)= \frac{15x^{14}+4x}{ \sqrt{x^{15}+2x^2+3} } [/latex] 18. [latex]f(x)= \frac{1}{ctgx}=tgx \\ \\ f'(x)= \frac{1}{cos^2x} [/latex] 19. [latex]f(x)=sin5x \\ f'(x)=5cos5x[/latex] 20. [latex]f(x)=cos( \frac{ \pi }{3}-2x )=cos \frac{ \pi }{3}cos2x+sin \frac{ \pi }{3}sin2x= \\ = \frac{1}{2}cos2x+ \frac{ \sqrt{3} }{2}sin2x \\ \\ f'(x)=-sin2x+ \sqrt{3}cos2x [/latex] 21. [latex]f(x)=10x^2- \frac{1}{x^3-2x} =10x^2-(x^3-2x)^{-1}\\ \\ f'(x)=20x+ \frac{1}{(x^3-2x)^2}*(3x^2-2)=20x+ \frac{3x^2-2}{(x^3-2x)^2} [/latex] 2. f(x)=-3x⁴+2x²+13 f ' (x)= -12x³ +4x = 4x(1-3x²) f '(-4)=4*(-4)(1-3*(-4)²)= -16(1-48)=-16*(-47)=752 [latex]f'( \frac{1}{2} )=4* \frac{1}{2}(-3*( \frac{1}{2} )^2+1)= \\ =2(- \frac{3}{4}+1 )=2* \frac{1}{4}= \frac{1}{2} [/latex]