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4 years ago

9

4. 6x² + 5 = 2x2 + 1

1 answer:

harkovskaia [24]4 years ago

3 0

Answer:

the answer is 31.16

Step-by-step explanation:

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Please help me answer this question

stealth61 [152]

The value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

<h3>Differentiation</h3>

From the question, we are to determine dy/dx for the given functions

(i) $x^{2} sin^{2}2x$

Let $u = x^{2}$

and

$v = sin^{2} 2x$

Also,

Let $w= sin2x$

∴ $v = w^{2}$

First, we will determine $\frac{dv}{dx}$

Using the Chain rule
$\frac{dv}{dx} = \frac{dv}{dw}.\frac{dw}{dx}$

$v = w^{2}$

∴ $\frac{dv}{dw} =2w$

Also,

$w= sin2x$

∴ $\frac{dw}{dx} =2cos2x$

Thus,

$\frac{dv}{dx} = 2w \times 2cos2x$

$\frac{dv}{dx} = 2sin2x \times 2cos2x$

$\frac{dv}{dx} = 4sin2x . cos2x$

Now, using the product rule

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

From above

$u = x^{2}$

∴ $\frac{du}{dx}=2x$

Now,

$\frac{dy}{dx} = x^{2} (4sin2x.cos2x)+ sin^{2}2x (2x)$

$\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $xy^{2}+y^{2}x^{3} +2=0$

Then,

$x.2y\frac{dy}{dx}+ y^{2}(1)+y^{2}.3x^{2} + x^{3}.2y\frac{dy}{dx} +0=0$

$2xy\frac{dy}{dx}+ y^{2}+3x^{2}y^{2} + 2x^{3}y\frac{dy}{dx} =0$

$2xy\frac{dy}{dx}+2x^{3}y\frac{dy}{dx} =- y^{2}-3x^{2}y^{2}$

$\frac{dy}{dx} (2xy+2x^{3}y)=- y^{2}(1+3x^{2})$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy+2x^{3}y}$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy(1+x^{2}) }$

$\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Hence, the value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Learn more on Differentiation here: brainly.com/question/24024883

#SPJ1

8 0

2 years ago

principal phillipi used a random sample of 20 students records to determine how far, in miles, students live from the school. Th

zzz [600]

To find the mean:

Take <span>3 4 5 3 4 5 6 5 4 3 2 3 4 5 6 4 8 4 3 2 and add them all together

=83

Now you divide 83 by the number of terms in the sample set, which is 20.

83/20 = 4.15

For rounding to the nearest tenth, look at the hundredths space, which is 5. Since it is 5 or higher, round the tenths up one.

final answer= 4.2 </span><span />

5 0

3 years ago

Read 2 more answers

Brandon has a 55-gallon fish tank. He estimates he can drain the tank at an average rate of 11 gallons per minute. In a linear m

Ket [755]

You would divide the number of gallons by the number of minutes

5 0

3 years ago

Simplify the expression 8+3z-z

Vaselesa [24]

Answer:

8+2z

Step-by-step explanation:

8+(3z-z=2z)=

8+2z

3 0

3 years ago

Charged at midnight. Which ordered pair is a viable

LiRa [457]

こんにちは、これを読んでいただきありがとうございます。私は英語が話せないので、あなたの質問には答えられないと言いたかっただけです。ごめんなさい。

4 0

3 years ago