find derivative of f(x)= x²+3x-6?
To find the derivative of the given function, f(x) = x² + 3x – 6, we can use the power rule
To find the derivative of the given function, f(x) = x² + 3x – 6, we can use the power rule. The power rule states that the derivative of x^n is given by n*x^(n-1), where n is any real number.
Let’s apply the rule to our function:
f'(x) = d/dx (x²) + d/dx (3x) – d/dx (6)
Taking the derivative term by term:
d/dx (x²) = 2x (since the power rule gives us 2*x^(2-1) = 2x)
d/dx (3x) = 3 (since the derivative of a constant multiplied by x is just the constant)
d/dx (6) = 0 (since the derivative of a constant is always zero)
Now, we can substitute our results back into f'(x):
f'(x) = 2x + 3 – 0
Simplifying, we have:
f'(x) = 2x + 3
Therefore, the derivative of f(x) = x² + 3x – 6 is f'(x) = 2x + 3.
More Answers:
Understanding the Increase of f ‘(x): Implications on Function Steepness and Growth RateUnderstanding the Power Rule for Differentiation: Finding the Derivative of f(x) = x² – 2
The Power Rule for Differentiation: Finding the Derivative of a Polynomial Function
Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded