Question

Y'=(9/x^3-2/x15x^4)'=?

Answer 1

3(3/x³-10x³)ʼ = -3(9/x⁴+30x²)

Answer 2

To find the derivative of the function y = (9/x^3 - 2/x^15x^4), you can use the rules of differentiation. First, simplify the expression:

y = 9/x^3 - 2/x^(3 + 15) = 9/x^3 - 2/x^18

Now, you can find the derivative using the power rule and the constant multiple rule. The power rule states that d/dx(x^n) = nx^(n-1), and the constant multiple rule states that d/dx(cf(x)) = c*f'(x), where c is a constant.

Let's find the derivative:

1. For the first term, 9/x^3: d/dx (9/x^3) = 9 * d/dx (x^(-3)) = 9 * (-3) * x^(-3-1) = -27/x^4

2. For the second term, -2/x^18: d/dx (-2/x^18) = -2 * d/dx (x^(-18)) = -2 * (-18) * x^(-18-1) = 36/x^19

Now, combine the derivatives of the two terms:

y' = (-27/x^4) + (36/x^19)

So, the derivative of y = (9/x^3 - 2/x^15x^4) is:

y' = -27/x^4 + 36/x^19