Find the derivative of g(x) = 2x^3+5x^2 -3x + 7
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
We have the function g(x) = 2x^3 + 5x^2 -3x + 7.
The derivative of x^n = n*x^(n - 1)
g(x) = 2x^3 + 5x^2 -3x + 7
=> g'(x) = 3*2*x^2 + 2*5*x - 3
=> g'(x) = 6x^2 + 10x - 3
The required derivative is 6x^2 + 10x - 3
hala718 | High School Teacher | (Level 1) Educator Emeritus
We have the function g(x) = 2x^3 + 5x^2 - 3x + 7.
We need to find the first derivative of g(x).
By definition we know that the derivative of ax^b = a*b*x^(b-1).
Then, we will apply the rule to all terms.
==> g'(x) = (2x^3)' + (5x^2)' -(3x)' + (7) '
==> g'(x) = 6x^2 + 10x - 3 + 0
Then, the first derivative is g'(x) and given by:
==> g'(x) = 6x^2 + 10x -3