Question

Differentiate 3cos x + 2log x + 21x + 5.

Answer 1

Answer:

- 3 Sinx + ( 2 / x ) + 21

Step-by-step explanation:

Given---> y = 3Cosx + 2 logx + 21x + 5

To find---> Derivative of given function

Solution---> We know that,

1) d / dx ( Cosx ) = - Sinx

2) d / dx ( log x ) = 1 / x

3) d / dx ( x ) = 1

4) d / dx ( Constant ) = 0

Now , returning to original problem,

Let,

y = 3 Cosx + 2 logx + 21x + 5

Differentiating with respect to x , we get,

dy/dx = d/dx ( 3Cosx + 2logx + 21x + 5 )

= d/dx(3Cosx ) + d/dx(2logx) + d/dx(21x) + d/dx( 5 )

Applying above formula , we get,

= - 3Sinx + ( 2 / x ) + 21 ( 1 ) + 0

= - 3Sinx + ( 2 / x ) + 21

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 ( tanx ) = Sec² x

6) d / dx ( Secx ) = Secx tanx

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

8) d / dx ( Cotx ) = - Cosec² x