найти производные указанных функций

y=x^4+3x^2+5

y=x^3-3x^2+x-1

3x^2+2x-5

y=2x^2+tgx

y=x^5-5x^2+sin x

y=e^x+ln x

y=x-ln x

y=cos x-sin x

y=√x + 1

-

x

y=log7x+3x

y=log3x-log5x

y=5x+2x

x2+5x

y=────

2-8x

y=3(x^2-2)

y=3x(x^2-2)

y=(1+sin x)(1+cos x)

y=tgx-2sin x

y=4(x^3-2)

y=4x (x^2-2)

y=ln x(x^2-1)

y=4^x log4x

1

Ответы и объяснения

2013-05-23T07:43:52+00:00

y` = 4x^3 +6x

y` = 3x^2-6x+1

y`= 6x+2

y`= 4x+ 1/ cos^2 x

y` = 5x^4-10x + cosx

y`= e^x + 1/x

y`= 1- 1/x

y`= -sinx +cos x

y`= 1/ (2*корень из х) - 1/ (х^2)

y`= 1/ (x ln 7) + 3

y`= 1/ (x ln 3) + 1/ (x ln 5)

y`= 5+2=7

y`= [(2x+5)(2-8x)+8(x^2+5x)] / (2-8x)^2 = (-8x^2+4x+10) / (2-8x)^2

y`= 6x

y`=9x^2-6

y`= cosx(1+cosx) - sinx(1+sinx)= cosx+cos^2 x-sinx-sin^2 x= cosx - sinx+ cos2x

y`= 1/( cos^2 x) - 2cosx

y`= 12x^2

y`= 12x^2-8

y`= 1/x * (x^2-1)+2x*lnx=(x^2-1) / x + 2x*lnx

y`= 4^x * ln4 * log4x + 4^x / (x*ln4)