Question

Find the derivative of ax² + bx +c /x^n
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Answer 1

To find the derivative of (ax² + bx + c) / x^n, use the quotient rule and simplify the resulting expression.

Step-by-step explanation:

The question is asking to find the derivative of the function (ax² + bx + c) / x^n. To do this, we use the quotient rule which states that the derivative of a function that is the quotient of two differentiable functions, U(x) and V(x), is given by:

(V(x)U'(x) - U(x)V'(x)) / [V(x)]^2

In this case, U(x) is ax² + bx + c and V(x) is x^n. The derivatives of U(x) and V(x) with respect to x are 2ax + b and nx^(n-1) respectively. Now we can apply the quotient rule:

1. Compute U'(x): 2ax + b
2. Compute V'(x): nx^(n-1)
3. Apply the quotient rule to find the derivative of (ax² + bx + c) / x^n:

(x^n(2ax + b) - (ax² + bx + c)(nx^(n-1))) / (x^n)^2

Simplify the expression to obtain the final derivative.