Question

Find dy/dx|x=-2 given that y = 5 - 4x² dy/dx| x=-2 =

Answer 1

So, dy/dx at x = - 2 is 16.

Derivatives:

A derivative is a fundamental concept in calculus, representing the rate of change of a function with respect to its independent variable (usually denoted as x). In simpler terms, it tells you how a function's output (y) changes as the input (x) changes.

To find dy/dx at the point x = - 2, we first need to find the derivative of the function y = 5 - 4x² concerning x, and then evaluate it at x = - 2.

Let's find dy/dx:

y = 5 - 4x²

Power rule:

To find dy/dx, we'll use the power rule for differentiation. The power rule states that if you have a term of the form axⁿ, then its derivative concerning x is:

`n* ax^(^n^-^1^)`

So, let's differentiate each term of the function y = 5 - 4x²:

The derivative of 5 concerning x is 0 (since it's a constant).

The derivative of -4x² concerning x is -8x (using the power rule).

Now, we have:

dy/dx = 0 - 8x = - 8x

Now, we need to evaluate dy/dx at x = - 2:

dy/dx | x = -2 = -8(-2) = 16

So, dy/dx at x = -2 is 16.