To find the derivative of the function [tex]\( f(x) = 2x^3 - x^2 - 5x + 3 \)[/tex], we need to differentiate each term of the function individually with respect to [tex]\( x \)[/tex].
Given:
[tex]\[ f(x) = 2x^3 - x^2 - 5x + 3 \][/tex]
1. For the first term [tex]\( 2x^3 \)[/tex]:
[tex]\[ \frac{d}{dx}(2x^3) = 2 \times 3x^{3-1} = 6x^2 \][/tex]
2. For the second term [tex]\( -x^2 \)[/tex]:
[tex]\[ \frac{d}{dx}(-x^2) = -1 \times 2x^{2-1} = -2x \][/tex]
3. For the third term [tex]\( -5x \)[/tex]:
[tex]\[ \frac{d}{dx}(-5x) = -5 \][/tex]
4. For the constant term [tex]\( 3 \)[/tex]:
[tex]\[ \frac{d}{dx}(3) = 0 \][/tex]
Now, combine these derivatives:
[tex]\[ f'(x) = 6x^2 - 2x - 5 \][/tex]
Thus, the derivative of the function [tex]\( f(x) = 2x^3 - x^2 - 5x + 3 \)[/tex] is:
[tex]\[ f'(x) = 6x^2 - 2x - 5 \][/tex]
