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2 years ago

Please someone help me out!!!!!!!!!!

Mathematics

1 answer:

german2 years ago

6 0

Answer:

Step-by-step explanation:

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Find thd <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D" id="TexFormula1" title="\frac{dy}{dx}" alt="\frac{dy}{dx}" a

NARA [144]

$x^3y^2+\sin(x\ln y)+e^{xy}=0$

Differentiate both sides, treating $y$ as a function of $x$ . Let's take it one term at a time.

Power, product and chain rules:

$\dfrac{\mathrm d(x^3y^2)}{\mathrm dx}=\dfrac{\mathrm d(x^3)}{\mathrm dx}y^2+x^3\dfrac{\mathrm d(y^2)}{\mathrm dx}$

$=3x^2y^2+x^3(2y)\dfrac{\mathrm dy}{\mathrm dx}$

$=3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(\sin(x\ln y)}{\mathrm dx}=\cos(x\ln y)\dfrac{\mathrm d(x\ln y)}{\mathrm dx}$

$=\cos(x\ln y)\left(\dfrac{\mathrm d(x)}{\mathrm dx}\ln y+x\dfrac{\mathrm d(\ln y)}{\mathrm dx}\right)$

$=\cos(x\ln y)\left(\ln y+\dfrac1y\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}$

Product and chain rules:

$\dfrac{\mathrm d(e^{xy})}{\mathrm dx}=e^{xy}\dfrac{\mathrm d(xy)}{\mathrm dx}$

$=e^{xy}\left(\dfrac{\mathrm d(x)}{\mathrm dx}y+x\dfrac{\mathrm d(y)}{\mathrm dx}\right)$

$=e^{xy}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)$

$=ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}$

The derivative of 0 is, of course, 0. So we have, upon differentiating everything,

$3x^2y^2+6x^3y\dfrac{\mathrm dy}{\mathrm dx}+\cos(x\ln y)\ln y+\dfrac{\cos(x\ln y)}y\dfrac{\mathrm dy}{\mathrm dx}+ye^{xy}+xe^{xy}\dfrac{\mathrm dy}{\mathrm dx}=0$

Isolate the derivative, and solve for it:

$\left(6x^3y+\dfrac{\cos(x\ln y)}y+xe^{xy}\right)\dfrac{\mathrm dy}{\mathrm dx}=-\left(3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}\right)$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^2+\cos(x\ln y)\ln y-ye^{xy}}{6x^3y+\frac{\cos(x\ln y)}y+xe^{xy}}$

(See comment below; all the 6s should be 2s)

We can simplify this a bit by multiplying the numerator and denominator by $y$ to get rid of that fraction in the denominator.

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x^2y^3+y\cos(x\ln y)\ln y-y^2e^{xy}}{6x^3y^2+\cos(x\ln y)+xye^{xy}}$

3 0

2 years ago

Find the derivative of the function. y = sin−1(6x + 1)

liraira [26]

If you don't know the derivative of the inverse of sine, you can use implicit differentiation. Apply sine to both sides:

$y=\sin^{-1}(6x+1)\implies\sin y=6x+1$

(true for <em>y</em> between -π/2 and π/2)

Now take the derivative of both sides and solve for it:

$\cos y\dfrac{\mathrm dy}{\mathrm dx}=6$

$\dfrac{\mathrm dy}{\mathrm dx}=6\sec y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\cos\left(\sin^{-1}(6x+1)\right)}$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\sqrt{1-(6x+1)^2}}$

7 0

2 years ago

How many times larger is 9 x 10^9 than 3 x 10^-4?

andrezito [222]

The larger value is 9 x 10^9
The smaller value is 3 x 10^(-4)

Divide the larger over the smaller
Doing so will have you divide the coefficients 9 and 3 (numbers in front of the "times ten to the..." portions) to get 9/3 = 3.
Then you'll also subtract the exponents: 9 minus (-4) = 9 - (-4) = 9 + 4 = 13

In summary so far, we got a coefficient of 3 and an exponent of 13

So the final answer is 3 x 10^13 (assuming you want scientific notation)

If you want to convert to standard notation, instead of scientific notation, move the decimal point in 3.0 thirteen spots to the right to get

30,000,000,000,000

there are 13 zeros (four groups of 3 plus one just after the 3) in that value above. This is the number 30 trillion

8 0

2 years ago

Why is 1/2 the same as 0.5

Basile [38]

Answer:

it’s because 0.50 is half of 100 and 1/2 is a reduced fraction of 50/100.

Step-by-step explanation:

5 0

1 year ago

Someone give me the answer

Mademuasel [1]

We want to begin with nine, which gives us as follows:

Then, we want to subtract:

9 -

And we are subtracting x:

9 - x

The expression is 9 - x for the steps in the image given.

Hope this helps!! :)

5 0

3 years ago