Pertanyaan

Jika diberikan fungsi maka nilai dari f'(x)=....

Jika diberikan fungsi $f open parentheses x close parentheses equals cos to the power of 4 invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses space$ maka nilai dari f'(x)= ....

$8 over open parentheses x minus 1 close parentheses squared sin cubed invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses sin invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses$
$8 over open parentheses x minus 1 close parentheses squared c o s to the power of 4 invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses sin invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses$
$8 over open parentheses x minus 1 close parentheses squared cos cubed invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses sin invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

Misalkan:

$y equals cos to the power of 4 invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses$

Misalkan: $z equals fraction numerator x plus 1 over denominator x minus 1 end fraction rightwards arrow y equals c o s to the power of 4 space z space$

$z equals fraction numerator x plus 1 over denominator x minus 1 end fraction space space table row cell right curly bracket u end cell row cell right curly bracket v end cell end table u equals x plus 1 space space semicolon u to the power of apostrophe equals 1 v equals x minus 1 space space semicolon v to the power of apostrophe equals 1 fraction numerator d z over denominator d x end fraction equals fraction numerator u to the power of apostrophe v minus u v to the power of apostrophe over denominator v squared end fraction equals fraction numerator 1 open parentheses x minus 1 close parentheses minus open parentheses x plus 1 close parentheses 1 over denominator open parentheses x minus 1 close parentheses squared end fraction fraction numerator d z over denominator d x end fraction equals negative 2 over open parentheses x minus 1 close parentheses squared y equals c o s to the power of 4 space z rightwards arrow fraction numerator d y over denominator d z end fraction equals negative 4 space s i n space z space c o s cubed space z f to the power of apostrophe open parentheses x close parentheses equals fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d z end fraction fraction numerator d z over denominator d x end fraction f to the power of apostrophe open parentheses x close parentheses equals open parentheses negative 4 space s i n space z space c o s cubed space z close parentheses open parentheses negative 2 over open parentheses x minus 1 close parentheses squared close parentheses f to the power of apostrophe open parentheses x close parentheses equals 8 over open parentheses x minus 1 close parentheses squared s i n space open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses cos cubed invisible function application open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses$