Determine the first second and third derivatives of 2x^13-3x^8+x^7-5x^3

Answer 1

The given function is f(x) = 2x^13 - 3x^8 + x^7 - 5x^3.

To find the first derivative, we differentiate each term of the function:
f'(x) = d(2x^13)/dx - d(3x^8)/dx + d(x^7)/dx - d(5x^3)/dx
= 26x^12 - 24x^7 + 7x^6 - 15x^2

To find the second derivative, we differentiate each term of the first derivative:
f''(x) = d(26x^12)/dx - d(24x^7)/dx + d(7x^6)/dx - d(15x^2)/dx
= 312x^11 - 168x^6 + 42x^5 - 30x

To find the third derivative, we differentiate each term of the second derivative:
f'''(x) = d(312x^11)/dx - d(168x^6)/dx + d(42x^5)/dx - d(30x)/dx
= 3432x^10 - 1008x^5 + 210x^4 - 30