# functionDifferentiate the function y = 5xcosx-sinx .

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### 2 Answers

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**

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**