Question

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$y= sqrt{sinx} , y= ( 5 x^{3x+1} +2 x^{2} )^{3}$

Answer 1

$y`=( sqrt{sinx})`= frac{1}{2 sqrt{sinx} } (sinx)`= frac{cosx}{2 sqrt{sinx} },$
$y`=((5 ^{3x+1}+2 x^{2}) ^{3})`=3 (5 ^{3x+1}+2 x^{2}) ^{2}cdot (5 ^{3x+1}+2 x^{2})`= \ =3 (5 ^{3x+1}+2 x^{2}) ^{2}cdot( (5 ^{3x+1})`+(2 x^{2})`)= \ =3 (5 ^{3x+1}+2 x^{2}) (5^{3x+1}cdot ln5cdot (3x+1)`+4x)= \ =3 (5 ^{3x+1}+2 x^{2}) (3ln5cdot5^{3x+1}+4x)$