Question

Найдите производную функции y=X cos x

Answer 1

Y'=x'cos x+x(cos x)'=cos x - x*sin x

Answer 2

Derivative of the Function y = x * cos(x)

To find the derivative of the function y = x * cos(x), we can use the product rule of differentiation. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by:

(d/dx)(u(x) * v(x)) = u'(x) * v(x) + u(x) * v'(x)

In this case, u(x) = x and v(x) = cos(x). Let's find the derivatives of u(x) and v(x) first:

u'(x) = 1 (the derivative of x with respect to x is 1) v'(x) = -sin(x) (the derivative of cos(x) with respect to x is -sin(x))

Now, we can apply the product rule:

(d/dx)(x * cos(x)) = u'(x) * v(x) + u(x) * v'(x) = 1 * cos(x) + x * (-sin(x)) = cos(x) - x * sin(x)

Therefore, the derivative of the function y = x * cos(x) is cos(x) - x * sin(x).