Đáp án:
$a) y'=-4(1-2x)-6(1-2x)^2-8(1-2x)^3\\
b) y'=2sinxcosx+3sin^2xcosx+4sin^3xcosx$
Giải thích các bước giải:
$a) y=(1-2x)^2+(1-2x)^3+(1-2x)^4\\
\Rightarrow y'=\left [(1-2x)^2+(1-2x)^3+(1-2x)^4 \right ]'\\
=\left [ (1-2x)^2\right ]'+\left [ (1-2x)^3 \right ]'+\left [ (1-2x)^4 \right ]'\\
=2.(1-2x).(1-2x)'+3(1-2x)^2.(1-2x)'+4.(1-2x)^3.(1-2x)'\\
=2(1-2x).(-2)+3(1-2x)^2.(-2)+4(1-2x)^3.(-2)\\
=-4(1-2x)-6(1-2x)^2-8(1-2x)^3\\
b) y=sin^2x+sin^3x+sin^4x\\
\Rightarrow y'=\left ( sin^2x+sin^3x+sin^4x \right )'\\
=(sin^2x)'+(sin^3x)'+(sin^4x)'\\
=2.sinx.(sinx)'+3sin^2x.(sinx)'+4sin^3x.(sinx)'\\
=2sinxcosx+3sin^2xcosx+4sin^3xcosx$
