find derivative of f(x)= x-x³?
To find the derivative of the function f(x) = x – x³, we can use the power rule for differentiation
To find the derivative of the function f(x) = x – x³, we can use the power rule for differentiation.
The power rule states that if we have a function g(x) = x^n, where n is a constant, then the derivative of g(x) is given by:
g'(x) = n * x^(n-1)
Applying the power rule to the function f(x) = x – x³, we differentiate each term separately:
The derivative of x with respect to x is 1:
d/dx (x) = 1
The derivative of -x³ with respect to x can be found using the power rule, where n = 3:
d/dx (-x³) = 3 * (-x)^(3-1) = -3x²
Now, the derivative of the entire function f(x) = x – x³ is given by the sum of the derivatives of each term:
f'(x) = d/dx (x) – d/dx (x³) = 1 – (-3x²) = 1 + 3x²
Therefore, the derivative of f(x) = x – x³ is f'(x) = 1 + 3x².
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