Question

How do you differentiate `f(x)=xcosx-sinx`?

Answer 1

`(df)/dx = -x sinx`

Explanation:

As the derivative is linear:

`(df)/dx = d/dx (xcosx) - d/dx(sinx) = d/dx (xcosx) - cosx`

applying now the product rule:

`(df)/dx = x d/dx (cosx) + (d/dx x)cosx - cosx`

`(df)/dx = -x sinx + cosx - cosx = -xsinx`