−21 is located to the Choose... of −20 on a number line. −19 is located to the Choose... of −20 on a number line.

Mathematics

1 answer:

german2 years ago

8 0

Answer:

21 is located to the Choose... of −20 on a number line. −19 is located to the Choose... of −20 on a number line.

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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.)

3 0

1 year ago

Question 21 on this pictured math sheet please. Have a great day!

Yuki888 [10]

Answer:

Step-by-step explanation:

$f(x) = 2x - 1.....(1) \\ g(x) = 3x + 5....(2) \\ plug \: x = 5 \: in \: (2) \\ g(5) = 3 \times 5 + 5 = 15 + 5 = 20 \\ \therefore \: f(g(5)) = 2 \times 20 - 1 = 40 - 1 = 39 \\ \\ \huge \red{ \boxed{\therefore \: f(g(5)) =39}}$