What is the derivative of #f(x) = arcsin(-10 x - 4)/9#?

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Answer 1 · 2018-01-15T15:02:11

#(dy)/(dx)=-10/(9sqrt(1-(10x+4)^2)#

As #y=f(x)=arcsin(-10x-4)/9#

#arcsin(-10x-4)=9y# or #sin(9y)=-10x-4#

i.e. #sin(9y)+10x+4=0#

and differentiating

#9cos(9y)(dy)/(dx)+10=0#

or #(dy)/(dx)=-10/(9cos(9y))#

= #-10/(9sqrt(1-sin^2(9y))#

= #-10/(9sqrt(1-(10x+4)^2)#