Tolong bantu ya Turunan aturan rantai .
Matematika
aidaadinda
Pertanyaan
Tolong bantu ya Turunan aturan rantai .
1 Jawaban
-
1. Jawaban whongaliem
[tex]y = (2x + 3)^{10} [/tex]
misal : u = 2x + 3
du/dx = 2
soal menjadi :
[tex]y = u^{10} ===\ \textgreater \ \frac{dy}{du} = 9. u^{9} [/tex]
[tex]y' = \frac{dy}{dx} [/tex]
[tex]= \frac{du}{dx} . \frac{dy}{dx} [/tex]
[tex]= 2 . 9 u^{9} [/tex]
[tex]= 18. u^{9} [/tex]
[tex]= 18 (2x + 3)^{9} [/tex]
[tex]2) y = (2 x^{2} + 1)^{5} [/tex]
misal : u = 2x² + 1 ⇒ du/dx = 4x
soal menjadi :
[tex]y = u^{5} ====\ \textgreater \ \frac{dy}{du} = 5. u^{4} [/tex]
[tex]y' = \frac{dy}{dx} [/tex]
[tex]= \frac{du}{dx} . \frac{dy}{du} [/tex]
[tex]= 4x . 5 u^{4} [/tex]
[tex]= 20x u^{4} [/tex]
[tex]= 20x (2 x^{2} + 1)^{4} [/tex]