Question

Y=cosx power tanx. Find dy/dx

Answer 1

Answer:

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Step-by-step explanation:

(cosx)^y= ln(sin y)^x

As we need to differentiate wrt x hence this is an example of explicit differentiation hence when we differentiate some function with variable y wrt x then using hain rule we also need to differentiate y as follows:-

y ln cosx= x ln siny

Using multiplication rule on both sides we get

-ysinx/cosx + ln cosx .dy/dx = ln siny + ycosy/siny. dy/dx

ln siny + y tanx= dy/dx( y coty-ln cosx)

dy/dx= (ln siny+y tanx)/(y coty- ln cosx)

Answer 2

Step-by-step explanation:

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