Ask question

Ask question

All categories

Vedmedyk [2.9K]

3 years ago

10

......................

1 answer:

pishuonlain [190]3 years ago

4 0

Answer:

$-1/x^2$

Step-by-step explanation:

First, let's simplify the expression on the right:

$1/\sqrt{x^2}=1/x$

Next, rewriting 1/x as x⁻¹, we can use the power rule to differentiate both sides with respect to x:

$y=x^{-1}\\dy/dx=d/dx(x^{-1})\\dy/dx=-x^{-2}=-1/x^2$

You might be interested in

62174 times 24724 Please help I don't understand plus I don't have a calculator.

docker41 [41]

When I multiply it’s is shows 1.53719

3 0

3 years ago

What is the equivalent mixed number to 23/4

lora16 [44]

5 3/4
5 remainder 3
Is the mixed number

4 0

3 years ago

Read 2 more answers

A particle moves on the hyperbola xy=18 for time t≥0 seconds. At a certain instant, y=6 and dydt=8. What is x that this instant?

professor190 [17]

Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let $x\cdot y = 18$ , we get an additional equation by implicit differentiation:

$x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (1)

From the first equation we find that:

$x = \frac{18}{y}$ (2)

By applying (2) in (1), we get the resulting expression:

$\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (3)

$y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}$

$\frac{dx}{dt} = -\frac{18}{y^{2}} \cdot \frac{dy}{dt}$

If we know that $y = 6$ and $\frac{dy}{dt} = 8$ , then the first derivative of x in time is:

$\frac{dx}{dt} = -\frac{18}{6^{2}} \cdot (8)$

$\frac{dx}{dt} = -4$

From (1) we determine the value of x at this instant:

$x\cdot \frac{dy}{dt} = -y\cdot \frac{dx}{dt}$

$x = -y\cdot \left(\frac{\frac{dx}{dt} }{\frac{dy}{dt} } \right)$

$x = -6\cdot \left(\frac{-4}{8} \right)$

$x = 3$

The value of x at this instant is 3.

4 0

3 years ago

Give me ans please......……………………

jeka57 [31]

hope it helps

it says I can't send if it has less than 20 characters why?

7 0

3 years ago

The students who went to summer camp voted for there favorite activities how many more students voted Viking than for fishing 21

Trava [24]

Simply subtract 21 from 9.

Your answer is 12 :)

5 0

3 years ago

Read 2 more answers