Differentiate the function y=5xcosx-sinx.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have y = 5*x*cos x - sin x.

We use the product rule to differentiate.

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

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

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

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

The required derivative of y = 5*x*cos x - sin x is y' = -5x sin x + 4 cos x

Top Answer

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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

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