Apakah derivatif fungsi y = sin (xy)?

Jawapan:

# dy / dx = (ycos (xy)) / (1-xcos (xy)) #

Penjelasan:

Menggunakan pembezaan implisit, peraturan produk, dan peraturan rantai, kita dapat

# d / dxy = d / dxsin (xy) #

# => dy / dx = cos (xy) (d / dx (xy)) #

# = cos (xy) x (d / dxy) + y (d / dxx) #

# = cos (xy) (xdy / dx + y) #

# = xcos (xy) dy / dx + ycos (xy) #

# => dy / dx - xcos (xy) dy / dx = ycos (xy) #

# => dy / dx (1-xcos (xy)) = ycos (xy) #

#:. dy / dx = (ycos (xy)) / (1-xcos (xy)) #