Question

Найдите производную функций

1)$y = cos^2x - sin^2x$

2)$y = 2 sin x * cos x$

3)y = sin 3x cos 5x + cos 3x sin 5x

4)y = cos 4x cos 6x - sin 4x sin 6x

5)$y = (1 - x^3)^5$

6)$y = sqrt{x^3 + 3x^2 - 2x + 1}$

7)$y = sin^3x$

8)$y = sqrt{ctgx}$

Answer 1

1
y=cos²x-sin²x=cos2x
y`=-2sin2x
2
y=2sinxcosx=sin2x
y`=2cos2x
3
3)y = sin 3x cos 5x + cos 3x sin 5x=sin(3x+5x)=sin8x
y`=8cos8x
4
4)y = cos 4x cos 6x - sin 4x sin 6x =cos(6x+4x)=cos10x
y`=-10sin10x
5
y=(1-x³)^5
y`=5(1-x³)^4*(-3x²)=-15x²(1-x³)^4
6
y=√(x³+3x²-2x+1)
$y`=(3x^2+6x-2)/2 sqrt{x^3+3x^2-2x+1}$
7
y=sin³x
y`=3sin²x*cosx
8
y=√ctgx
$y`=-1/(2 sqrt{ctgx} sin^2x)$