Find the second derivative for y=(x+2)/(x-3)

Answers

Answer 1

Answer: Let's find the first derivative.

Using quotient rule

$f(x)=(g(x))/(h(x))$

$f'(x)=(g'(x)*h(x)-g(x)*h'(x))/(h^2(x))$

then:

$y=(x+2)/(x-3)$
$f(x)=y$

$g(x)=x+2$

$g'(x)=1$

$h(x)=x-3$

$h'(x)=1$

Let's replace

$f'(x)=(g'(x)*h(x)-g(x)*h'(x))/(h^2(x))$

$y'=(1*(x-3)-(x+2)*1)/((x-3)^2)$

$y'=(x-3-x-2)/((x-3)^2)$

$\boxed{y'=(-5)/((x-3)^2)}$

the second derivative is the derivative of our first derivative.

$y'=(-5)/((x-3)^2)$

We can write this function as

$y'=-5*(x-3)^(-2)$

now we have to use the Chain rule's

$f(u)=-5u^(-2)$

and

$g(x)=x-3$

$f[g(x)]=-5*(x-3)^(-2)$

then

$f'[g(x)]=f'(u)*g'(x)$

$f'(u)=-5*(-2)*u^(-3)=10*u^(-3)$

$g'(x)=1$

$f'[g(x)]=f'(u)*g'(x)$

Let's replace

$f'[g(x)]=10*u^(-3)*1$

Let's change u by $(x-3)$

$f'[g(x)]=10*u^(-3)$

$f'[g(x)]=10*(x-3)^(-3)$

$\boxed{\boxed{y''=(10)/((x-3)^(3))}}$

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Need help with a math question

Answers

Answer:

Step-by-step explanation:

3 digits ^4 number options

3^4=81

If you vertically stretch the quadratic parent function, f(x) = 2^x, by a factor of 3, what is the equation of the new function?

Answers

If you stretch on the y-axis then you are increasing/decreasing values at a every x.

The new function is therefore:

$g(x)=3\cdot2^x$

Hope this helps.

If pencils sell at 6 for 59 cents how many pencils can be bought for 2.95

Answers

We already know from the given data that 6 pencils can be bought for 59 cents. We have to determine the number of pencils that can be bought for $2.95.
So
Price of 6 pencils = 59 cents.
Price of 1 pencil = (59/6) cents
   = 9.83 cents
Now total amount in hand for buying pencils = $2.95
   = 295 cents
Then the number of pencils that can be bought for 295 cents = (295/9.83)
   = 30.01
So the maximum number of pencils that can be bought for $2.95 is 30 pencils.

Answer:

Step-by-step explanation:

What is the 289345.29 x 13.4

Answers

3,877,226.886

that the answer

What is the point that lies on a graph for 10y=3x-11. Is it A (2,-.5) B (4,1) C (6,16.3). Or D (8,23)?

Answers

case A : x=2, y=-5
so putting the values of x and y in the equation, we get 10y -3x should be -11
so, 10* (-5) - 3 *2 = -50-6 = -56
case B , value of equation = 10*4 - 3*1 = 37
case C, value of equation = 10*6 -3*16.3 = -11.1
Case D, value of equation = 10*8-3*23 = 11
Ans will be C

I'm very lost on this, can I get some help? This should be easier than it actually is

Answers

Answer:(4,8)

Step-by-step explanation: you go down 4 you go across 8 you get your answer

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