Question

Apply the sum and difference rules to combine Question Find the derivative of f(x)=6x6−4x5+1. Provide your answer below: f′(x)=

Answer 1

To find the derivative of the function f(x) = 6x^6 - 4x^5 + 1, you can apply the power rule for differentiation to each term separately. The power rule states that if you have a term of the form ax^n, the derivative is n * ax^(n-1). Here's how you differentiate each term:

1. Differentiate the first term, 6x^6:

f'(x) = 6 * 6x^(6-1) = 36x^5

2. Differentiate the second term, -4x^5:

f'(x) = -4 * 5x^(5-1) = -20x^4

3. The derivative of a constant term (1) is zero:

f'(x) = 0

Now, combine these derivatives together since they are individual terms in the function:

f'(x) = 36x^5 - 20x^4

So, the derivative of f(x) is f'(x) = 36x^5 - 20x^4.

Explanation: