Question

Y=5x-6x^4+8x^5^ - степеньНайдите y'

Answer 1

$y=5x-6x^4+8x^5\\y'=5-6*4x^3+8*5x^4=5-24x^3+40x^4$

Answer 2

To find the derivative of the function y with respect to x, denoted as y', we need to differentiate each term of the function with respect to x using the rules of differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1). Here's the step-by-step process to find y':

Given function: y = 5x - 6x^4 + 8x^5

Step 1: Differentiate the first term (5x) with respect to x: (d/dx) [5x] = 5 * d/dx(x) = 5 * 1 = 5

Step 2: Differentiate the second term (-6x^4) with respect to x: (d/dx) [-6x^4] = -6 * d/dx(x^4) = -6 * 4x^(4-1) = -6 * 4x^3 = -24x^3

Step 3: Differentiate the third term (8x^5) with respect to x: (d/dx) [8x^5] = 8 * d/dx(x^5) = 8 * 5x^(5-1) = 8 * 5x^4 = 40x^4

Step 4: Combine the derivatives of each term to find y': y' = 5 - 24x^3 + 40x^4

So, the derivative of y with respect to x (y') is: y' = 5 - 24x^3 + 40x^4