What is the first derivative of the function x*sinx+cosx ?
We have to find the first derivative of f(x) = x*sin x + cos x
f'(x) = x*(sin x )' + x'* sin x + (cos x)'
=> f'(x) = x cos x + sin x - sin x
=> f'(x) = x cos x
Therefore the first derivative of x*sin x+cos x is x cos x.
We'll differentiate the function with respect to x.
We'll note the function as y = f(x):
dy/dx = d/dx(x)*sinx + x*d/dx(sin x) + d/dx(cosx)
dy/dx = sin x + x*cosx - sin x
We'll eliminate like terms
dy/dx = x*cosx
The first derivative of the function f(x) is:
f'(x) = x*cos x