Pertanyaan

Tentukan f ( x ) jika diketahui fungsi-fungsi berikut, b. f ( x ) = ( − 4 x + 1 ) − 3 ⋅ ( 6 x + 5 ) − 2

Tentukan $f (x)$ jika diketahui fungsi-fungsi berikut,

b. $f (x) = (- 4 x + 1)^{- 3} \cdot (6 x + 5)^{- 2}$

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M. Rochmat

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Jawaban terverifikasi

Jawaban

i, Jika maka f ′ ( x ) = ( 1 − 4 x ) 4 ( 6 x + 5 ) 3 120 x + 48

i, Jika

straight f left parenthesis straight x right parenthesis equals left parenthesis negative 4 straight x plus 1 right parenthesis to the power of negative 3 end exponent times left parenthesis 6 straight x plus 5 right parenthesis to the power of negative 2 end exponent

maka

f^{'} (x) = \frac{120 x + 48}{( 1 - 4 x ) ^{4} ( 6 x + 5 ) ^{3}}

Pembahasan

Menentukan turunan fungsi aljabar denganaturan rantai; Misalkan: Maka: f ( x ) f ( x ) f ′ ( x ) = = = = = = = = = ( − 4 x + 1 ) − 3 ⋅ ( 6 x + 5 ) − 2 u ⋅ v u ⋅ v ′ + u ′ ⋅ v ( − 4 x + 1 ) − 3 ⋅ ( − 12 ( 6 x + 5 ) − 3 ) + 12 ( − 4 x + 1 ) − 4 ⋅ ( 6 x + 5 ) − 2 − 12 ( ( − 4 x + 1 ) − 3 ) ( 6 x + 5 ) − 3 ) + 12 ( − 4 x + 1 ) − 4 ⋅ ( 6 x + 5 ) − 2 − 12 ( ( − 4 x + 1 ) − 4 ) ( 6 x + 5 ) − 3 ) (( − 4 x + 1 ) − ( 6 x + 5 ) − 12 ( ( − 4 x + 1 ) − 4 ) ( 6 x + 5 ) − 3 ) ( − 10 x − 4 ) ( − 4 x + 1 ) 4 ( 6 x + 5 ) 3 − 12 ( − 10 x − 4 ) ( 1 − 4 x ) 4 ( 6 x + 5 ) 3 120 x + 48 Jadii, Jika maka f ′ ( x ) = ( 1 − 4 x ) 4 ( 6 x + 5 ) 3 120 x + 48

Menentukan turunan fungsi aljabar dengan aturan rantai;

Misalkan:

Maka:

$f (x) f (x) f^{'} (x) = = = = = = = = = (- 4 x + 1)^{- 3} \cdot (6 x + 5)^{- 2} u \cdot v u \cdot v^{'} + u^{'} \cdot v (- 4 x + 1)^{- 3} \cdot (- 12 (6 x + 5)^{- 3}) + 12 (- 4 x + 1)^{- 4} \cdot (6 x + 5)^{- 2} - 12 ((- 4 x + 1)^{- 3}) (6 x + 5)^{- 3}) + 12 (- 4 x + 1)^{- 4} \cdot (6 x + 5)^{- 2} - 12 ((- 4 x + 1)^{- 4}) (6 x + 5)^{- 3}) ((- 4 x + 1) - (6 x + 5) - 12 ((- 4 x + 1)^{- 4}) (6 x + 5)^{- 3}) (- 10 x - 4) \frac{- 12 ( - 10 x - 4 )}{( - 4 x + 1 ) ^{4} ( 6 x + 5 ) ^{3}} \frac{120 x + 48}{( 1 - 4 x ) ^{4} ( 6 x + 5 ) ^{3}}$

Jadii, Jika straight f left parenthesis straight x right parenthesis equals left parenthesis negative 4 straight x plus 1 right parenthesis to the power of negative 3 end exponent times left parenthesis 6 straight x plus 5 right parenthesis to the power of negative 2 end exponent maka $f^{'} (x) = \frac{120 x + 48}{( 1 - 4 x ) ^{4} ( 6 x + 5 ) ^{3}}$