functionDifferentiate the function y = 5xcosx-sinx .

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to differentiate y = 5x*cos x - sin x

Use the product rule

y' = 5x*(cos x)' + 5(x)'*cos x - (sin x)'

=> y' = -5x* sin x + 5*cos x - cos x

=> y' = 4*cos x - 5x*sin x

The required derivative is 4*cos x - 5x*sin x

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll differentiate the function with respect to x. We'll apply product rule:

dy/dx = d/dx(5x)*cosx + 5x*d/dx(cosx) - d/dx(sinx)

dy/dx = 5cosx + 5x(-sinx) - cos x

We'll factorize by cos x like terms:

dy/dx = cos x(5 - 1) + 5x(-sinx)

dy/dx = 4cos x - 5xsinx

The result of differentiating the function y is:

dy/dx = 4cos x - 5xsinx

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question