Question

b) Find the derivative of
cos
sin x
w.r.t. 'X' using the rules of differentiation.​

Answer 1

Answer:

5x⁴ Sinx - x⁵ Cosx + 1 / Sin²x

Step-by-step explanation:

Given---> y = ( x⁵ - Cosx ) / Sinx

To find---> Derivative of given function

Solution---> ATQ,

y = ( x⁵ - Cosx ) / Sinx

Differentiating with respect to x,

=> dy/dx = d/dx { ( x⁵ - Cosx ) / Sinx }

We have division rule of differentiation as follows

d/dx( u / v ) = ( v du/dx - u dv/dx ) / v²

applying this formula here , we get

= Sinxd/dx(x⁵- Cosx) - (x⁵-Cosx )d/dx(Sinx) / Sin²x

We have some formulee of differentiation as follows,

1) d/dx ( xⁿ ) = nxⁿ⁻¹

2) d/dx ( Sinx ) = Cosx

3) d/dx ( Cosx ) = - Sinx

Applying these formulee here , we get,

= Sinx ( 5x⁴ + Sinx ) - (x⁵ - Cosx ) Cosx / Sin²x

= ( 5x⁴Sinx + Sin²x - x⁵Cosx + Cos²x ) / Sin²x

= ( 5x⁴Sinx - x⁵Cosx + Sin²x + Cos²x ) / Sin²x

We have an identity of trigonometery ,

Sin²θ + Cos²θ = 1 , applying it here we get,

dy / dx = ( 5x⁴Sinx - x⁵ Cosx + 1 ) / Sin²x