Question

Найти производную: 1.) (x^2+2x+1)(x+3) 2.) (2x^2+x)^2+(1-x)^3 3.) sqrt(x-2)+cos(x^2-2x)

Answer 1

1)y=(x²+2x+1)(x+3);⇒
y¹=(x²+2x+1)¹(x+3)+(x²+2x+1)(x+3)¹=(2x+2)(x+3)+(x²+2x+1)·1=
=2x²+2x+6x+6+x²+2x+1=3x²+10x+7;
2)y=(2x²+x)²+(1-x)³=4x⁴+4x³+x²+1-3x+3x²-x³=4x⁴+3x³+4x²-3x+1;
y¹=4·4x³+3·3x²+4·2x-3=16x³+9x²+8x-3;
3)y=√(x-2)+cos(x²-2x)=(x-2)¹/²+cos(x²-2x);
y¹=(1/2)·(x-2)⁻¹/²·1+(2x-2)·(-sin(x²-2x))=1/(2√(x-2)) -(2x-2)·sin(x²-2x)