What is 2000(2000^2000)?

Mathematics

1 answer:

Harrizon [31]3 years ago

7 0

Answer:

A. 2000²⁰⁰¹

Step-by-step explanation:

2000(2000²⁰⁰⁰) = 2000²⁰⁰⁰+1 = 2000²⁰⁰¹

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Cindys grandmother is five times her age. Find each of their ages if the sum of their ages is 90

yan [13]

Answer:

cindy=15 grandmother=75

Step-by-step explanation:

90 divide 6 equal to 15

6 0

3 years ago

Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)