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nlexa [21]
1 year ago
15

How do I find dy/dx of the following?

Mathematics
1 answer:
Pachacha [2.7K]1 year ago
5 0

Answer:

\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}

Step-by-step explanation:

                      y \ = \ x^{3} \ - \ \displaystyle\frac{1}{\sqrt{x}} \ + \ \displaystyle\frac{3}{x^{4}} \\ \\ y \ = \ x^{3} \ - \ x^{-\frac{1}{2}} \ + \ 3x^{-4} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{3 \ - \ 1} \ - \ \left(-\displaystyle\frac{1}{2}\right)x^{-\frac{1}{2} \ - \ 1} \ + \ \left(-4 \ \times \ 3\right)x^{-4-1}

                       \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2}x^{-\frac{3}{2}} \ - \ 12x^{-5} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}

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5 0
3 years ago
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The Eiffel Tower is 324 m tall. If a tourist is looking at it from 100 m away from the base,
romanna [79]

Answer:

80,94º

Step-by-step explanation:

What I've done is, first draw a triangle with a 90º angle and write down the height (324m) and the tourist's distance (100m).

So I calculated the tangent of the angle of the tourist.

The formula is tan=Oposite side/adjacent

tan=\frac{opposite side}{adjacent}

tan=\frac{324}{100} =3.24

And now with your calculator you press "shift" and "tan". Then introduce 3,24 and it will give you the result (80,94º).

I hope it helped.

4 0
2 years ago
Which statements are true?
castortr0y [4]

Answer:


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5 0
3 years ago
If the common difference of an ap is 3/2 and its 20 th term 35×1/2 find first term and 15 th term
Lady bird [3.3K]

Answer:

Step-by-step explanation:

d = 3/2

a₂₀ = a₁+19d

35/2 = a₁ + 19×3/2

a₁ = 35/2 - 19×3/2 = -11

a₁₅ = a₁+14d = -11 + 14×3/2 = 10

4 0
2 years ago
If (x + 1)(x-3) = 5, then which of the following statements is true?
bixtya [17]

Answer:

x=−2 or x=4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x2−2x−3=5

Step 2: Subtract 5 from both sides.

x2−2x−3−5=5−5

x2−2x−8=0

Step 3: Factor left side of equation.

(x+2)(x−4)=0

Step 4: Set factors equal to 0.

x+2=0 or x−4=0

x=−2 or x=4

5 0
3 years ago
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