Câu hỏi

Cho hàm số xác định với mọi x > 0 . Tính được kết quả:

Cho hàm số g not stretchy left parenthesis x not stretchy right parenthesis equals integral subscript square root of x end subscript superscript x to the power of 2 end exponent end superscript square root of t sin invisible function application t d t xác định với mọi $x > 0$ . Tính g to the power of straight prime end exponent not stretchy left parenthesis x not stretchy right parenthesis được kết quả:

$g to the power of straight prime left parenthesis x right parenthesis equals x squared sin invisible function application open parentheses x squared close parentheses minus fraction numerator sin invisible function application left parenthesis square root of x right parenthesis over denominator fourth root of x end fraction$
$g to the power of straight prime left parenthesis x right parenthesis equals 2 x squared sin invisible function application open parentheses x squared close parentheses minus fraction numerator sin invisible function application left parenthesis square root of x right parenthesis over denominator 2 fourth root of x end fraction$
$g to the power of straight prime left parenthesis x right parenthesis equals 2 x squared sin invisible function application open parentheses x squared close parentheses minus fraction numerator sin invisible function application left parenthesis square root of x right parenthesis over denominator fourth root of x end fraction$
$g to the power of straight prime left parenthesis x right parenthesis equals x squared sin invisible function application open parentheses x squared close parentheses minus fraction numerator sin invisible function application left parenthesis square root of x right parenthesis over denominator 2 fourth root of x end fraction$

R. Roboctvx107

Giáo viên

Xác nhận câu trả lời

Giải thích

Ta gọi là nguyên hàm của t sin t Ta có

Ta gọi F not stretchy left parenthesis t not stretchy right parenthesis là nguyên hàm của $t sin t$

Ta có

$not stretchy rightwards double arrow g to the power of straight prime left parenthesis x right parenthesis equals 2 x squared F to the power of straight prime open parentheses x squared close parentheses minus fraction numerator 1 over denominator 2 square root of x end fraction F to the power of straight prime left parenthesis square root of x right parenthesis$

$not stretchy rightwards double arrow g to the power of straight prime left parenthesis x right parenthesis equals 2 x squared sin invisible function application open parentheses x squared close parentheses minus fraction numerator sin invisible function application left parenthesis square root of x right parenthesis over denominator 2 fourth root of x end fraction$