Question

derive (x+5)^3

Answer 1

what a lot of work!
And you still got it wrong

y = (x+5)^3
y' = 3(x+5) = 3x^2 + 30x + 75

Answer 2

To derive the expression (x+5)^3, we can use the chain rule.

First, let's expand the expression:

(x+5)^3 = (x+5)(x+5)(x+5) = (x^2 + 10x + 25)(x+5)

Now, let's take the derivative:

d/dx [(x^2 + 10x + 25)(x+5)]

Using the product rule, the derivative of the first term (x^2 + 10x + 25) is:

(2x + 10)(x+5)

And, the derivative of the second term (x+5) is simply 1.

Now, using the product rule again, we have:

[(2x + 10)(x+5)](x+5) + (x^2 + 10x + 25)(1)

Simplifying this expression gives us the derivative of (x+5)^3:

(2x + 10)(x+5)^2 + (x^2 + 10x + 25)

Answer 3

Apologies for the mistake in my previous response. You are correct. The correct derivative of (x+5)^3 is indeed 3x^2 + 30x + 75. Thank you for pointing out the error.