Question

Найдите f'x если fx=x^-3- 0.5cos 2x

Answer 1

f'(x)=(x^3-3-0,5cos(2x))'=3x^2-sin(2x)

Answer 2

To find the derivative of the function f(x) = x^(-3) - 0.5cos(2x) with respect to x (f'(x)), we'll differentiate each term of the function using standard differentiation rules. Let's go step by step:

1. Differentiate the term x^(-3): The derivative of x^n, where n is a constant, is given by d/dx(x^n) = nx^(n-1). So, d/dx(x^(-3)) = -3x^(-3-1) = -3*x^(-4) = -3/x^4.

2. Differentiate the term -0.5cos(2x): The derivative of cos(ax), where a is a constant, is given by d/dx(cos(ax)) = -asin(ax). So, d/dx(-0.5cos(2x)) = -0.5(-2)*sin(2x) = sin(2x).

Now, combining the derivatives of both terms, we get:

f'(x) = d/dx(x^(-3)) - d/dx(0.5cos(2x)) f'(x) = -3/x^4 - sin(2x)

So, the derivative of the function f(x) is f'(x) = -3/x^4 - sin(2x).