What is the first derivative of the function x*sinx+cosx ?

Asked on by jane1992

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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 

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