Find the derivative of sinxcosx using first principles

Let f (x) = sin x cos x. Accordingly, from the first principle,

 

  • 10

use sin2x formula first  i.e multiply and divide by 2.i found out the solution but word limit problem

  • 1

 2sin(x+h)  cos(x+h)  - 2sinx cosx / 2h

  • 7

 sin(2x+2h) - sin2x   /2h

  • 4

 now sin a- sinb formula the ans is cos2x

  • 10

d/dx(sinx.cosx)
=sinx.d/dx(cosx) + cosx.d/dx(sinx)
=sinx(-sinx) + cosx(cosx)
=cos2x

  • 10
What are you looking for?