Question

D/dx sinx•logx find the differentiation of these question

Answer 1

Answer:

( Sinx + x logx Cosx ) / x

Step-by-step explanation:

To find -----> Differentiation of Sinx logx

Solution------> We have a formula , product rule of differentiation as follows ,

d/dx ( u v ) = u dv/dx + v du/dx

Let,

y = Sinx logx

Differentiatig with respect to x , we get,

=> dy / dx = d/dx ( Sinx logx )

Applying product rule of differentiation , we get,

= Sinx d/dx ( logx ) + logx d/dx ( Sinx )

= Sinx ( 1 / x ) + logx ( Cosx )

= ( Sinx + x logx Cosx ) / x

Additional information---->

1) d/dx ( xⁿ ) = n xⁿ⁻¹

2) d / dx ( eˣ ) = eˣ

3) d / dx ( aˣ ) = aˣ loga

4) d / dx ( Sinx ) = Cosx

5) d / dx ( Cosx ) = - Sinx

6) d / dx ( tanx ) = Sec²x

7) d / dx ( Secx ) = Secx tanx

8) d / dx ( Cosecx ) = - Cosecx Cotx

9) d / dx ( Cotx ) = - Cosec²x