Apakah derivatif (sinx) ^ tanhx? Jika anda membantu saya, saya amat berterima kasih ...

Jawapan:

#sin (x) ^ tanh (x) * (1-tanh ^ 2 (x)) * ln (sin (x)) + "

# "" sin (x) ^ (tanh (x) -1) * tanh (x) * cos (x) #

Penjelasan:

# "Derivatif" #

#f (x) ^ g (x) #

# "adalah formula yang sukar diingati." #

# "Jika anda tidak dapat mengingat dengan baik, anda boleh menyimpulkannya seperti berikut:" #

# x ^ y = exp (y * ln (x)) #

# => f (x) ^ g (x) = exp (g (x) * ln (f (x))) #

(x)) '= exp (g (x) * ln (f (x))) (g (x) * ln (f (x)

# "(aturan rantaian + terbitan exp (x))" #

f (x)) (g '(x) * ln (f (x)) + g (x)

(x) * f '(x) * ln (f (x)) + f (x) ^ (g (x) - 1) #

# "Di sini kita ada" #

#f (x) = sin (x) => f '(x) = cos (x) #

#g (x) = tanh (x) => g '(x) = 1 - tanh ^ 2 (x) #

# = sin (x) ^ tanh (x) * (1-tanh ^ 2 (x)) * ln (sin (x)

#sin (x) ^ (tanh (x) -1) * tanh (x) * cos (x) #