Differentiate from first principles, with respect to x, (3x\(^2\) + 2x - 1)
Differentiation is a mathematical process that allows us to find the rate of change of a function at a certain point. To differentiate the function (3x2 + 2x - 1) with respect to x from first principles, we'll use the power rule of differentiation.
The power rule states that if we have a term in the form of xn, then its derivative is given by nx(n-1).
Applying this rule to the function (3x2 + 2x - 1), we get:
d/dx (3x2) = 6x
d/dx (2x) = 2
The derivative of a constant is 0, so:
d/dx (-1) = 0
Putting it all together, we find that the derivative of (3x2 + 2x - 1) with respect to x is:
d/dx (3x2 + 2x - 1) = 6x + 2
So, the rate of change of the function (3x2 + 2x - 1) at any point x is given by 6x + 2.
Differentiation is a mathematical process that allows us to find the rate of change of a function at a certain point. To differentiate the function (3x2 + 2x - 1) with respect to x from first principles, we'll use the power rule of differentiation.
The power rule states that if we have a term in the form of xn, then its derivative is given by nx(n-1).
Applying this rule to the function (3x2 + 2x - 1), we get:
d/dx (3x2) = 6x
d/dx (2x) = 2
The derivative of a constant is 0, so:
d/dx (-1) = 0
Putting it all together, we find that the derivative of (3x2 + 2x - 1) with respect to x is:
d/dx (3x2 + 2x - 1) = 6x + 2
So, the rate of change of the function (3x2 + 2x - 1) at any point x is given by 6x + 2.