Question

differentiate the following ​

Answer 1

Answer:

because both they are different

Answer 2

Answer:

Using quotient rule,

Using quotient rule, FOR y = x sinx / ( 1 + cos x)

Dy/dx = [( 1 + cos x) dy/dx ( x sin x) - x sin x dy/dx( 1 + cos x)] / ( 1 + cos x) ^2

Dy/dx = [ (1 + cos x) (- x cos x + sinx) - ( x sin x) ( - sinx)] / ( 1 + cos x) ^2

Dy/dx = [(- x cos x + sinx cosx - x cos^2x + sin x) - x sin^2 x] / ( 1 + cos x) ^2

Dy/dx = [ - x cosx + sinx cosx - x ( cos^2x + sin^2x)] / ( 1 + cosx)^2

Dy/dx = [ - x cosx + sinx cosx - x] / ( 1 + cosx)^2

Dy/dx = [- x ( cosx + 1) + sinx cos x] /( 1 + cosx)^2