Find the instantaneous rate of change of y with respect to x when x = 15 for the function y = 5x2 − 2x
Well, you've come to the right bot for some clownish explanations! To find the instantaneous rate of change of y with respect to x, we need to take the derivative of the function y = 5x^2 - 2x with respect to x.
So, let's put our clown hat on and get ready to differentiate! Taking the derivative term by term, we get:
dy/dx = d(5x^2)/dx - d(2x)/dx
Now, let's differentiate each term separately. The derivative of 5x^2 with respect to x is 10x (using the power rule for derivatives), and the derivative of 2x with respect to x is simply 2 (since the derivative of x with respect to x is 1).
Putting it all together, we have:
dy/dx = 10x - 2
Now, all we need to do is plug in the given x-value of 15 to find the instantaneous rate of change of y at that point. Let's calculate!
dy/dx = 10(15) - 2
= 150 - 2
= 148
So, when x = 15, the instantaneous rate of change of y with respect to x is 148. You could say it's like the clown car going full throttle at a hilarious speed!
To find the instantaneous rate of change of y with respect to x, we need to find the derivative of the function y = 5x^2 - 2x.
First, let's differentiate the function with respect to x:
y' = d/dx(5x^2 - 2x)
Using the power rule for differentiation, the derivative of x^2 is 2x, and the derivative of x is 1. Therefore, the derivative becomes:
y' = 10x - 2
Now, we need to find the value of the derivative at x = 15:
y'(15) = 10(15) - 2
= 150 - 2
= 148
Therefore, the instantaneous rate of change of y with respect to x when x = 15 is 148.
To find the instantaneous rate of change of y with respect to x, we need to find the derivative of the function y with respect to x, and then evaluate it at x = 15.
First, let's find the derivative of y = 5x^2 - 2x. We can use the power rule for differentiation, which states that the derivative of x^n is nx^(n-1).
The derivative of 5x^2 is:
d/dx (5x^2) = 2 * 5x^(2-1) = 10x
The derivative of -2x is:
d/dx (-2x) = -2
Now, let's find the derivative of the entire function by summing the derivatives of each term:
dy/dx = 10x - 2
To find the instantaneous rate of change of y with respect to x at x = 15, we substitute x = 15 into the derivative equation:
dy/dx = 10x - 2
dy/dx = 10(15) - 2
dy/dx = 150 - 2
dy/dx = 148
Therefore, the instantaneous rate of change of y with respect to x when x = 15 is 148.
I think you meant to type
y = 5x^2 - 2x
if so, then
dy/dx = 10x - 2
and if x = 15
dy/dx = 10(15) - 2 = 148