The value of the square root function after differentiation is
.
The given equation is :
x³√4y = 5
Now we will use implicit differentiation
![\implies3x^2\sqrt{4y} \ \ dx +x^3\times 2(-\frac{1}{\sqrt y}) =0\\\\\implies6x^2\sqrt{y}\ dx-2\frac{x^3}{\sqrt y}\ dy=0\\\\\implies \frac{dy}{dx}= \frac{3}{x}](https://tex.z-dn.net/?f=%5Cimplies3x%5E2%5Csqrt%7B4y%7D%20%5C%20%20%5C%20dx%20%2Bx%5E3%5Ctimes%202%28-%5Cfrac%7B1%7D%7B%5Csqrt%20y%7D%29%20%3D0%5C%5C%5C%5C%5Cimplies6x%5E2%5Csqrt%7By%7D%5C%20dx-2%5Cfrac%7Bx%5E3%7D%7B%5Csqrt%20y%7D%5C%20dy%3D0%5C%5C%5C%5C%5Cimplies%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B3%7D%7Bx%7D)
In mathematics, the derivative of a simple function that resembles a real variable measures how sensitive the function's value (or output value) is to changes in the underlying assumption (input value). The derivative is the fundamental tool in calculus.
The value of y from the equation is :
y = 25/4 x⁻³
now if we differentiate this function we get the same result.
y'=3/x
Hence we can see that the value of both the solution are equal.
A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's point with regard to time.
Hence the required solution of the differentiation is ![\frac{dy}{dx}= \frac{3}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B3%7D%7Bx%7D)
to learn more about square root visit:
brainly.com/question/15208820
#SPJ9
Let x = baby dinosaurs
y = adult dinosaurs
equation 1
total paintings = 15 painting x + 7 paintings y
equation 2
baby dinosaurs = 3 times adult
x= 3y
substitute x= 3y to equation 1
y = 4
x = 12
There are 12 baby dinosaurs and 4 adult dinosaurs in a herd with 208 total paintings
Factorise 4b² + 16b ⇒ 4b(b+4)
expand (a-1)(a-2) ⇒ a(a-2) - 1(a-2) ⇒ a² - 2a - 1a + 2 ⇒a² - 3a + 2
factorise x² + 8x + 7 ⇒(x + 1) (x + 7)
evaluate y⁶ / y² ⇒ y * y * y * y * y * y / y * y = y⁴
if x = -1 and y = 5, find z when z = x² + 2y² ;
z = -1² + 2(5²) ⇒ 1 + 2(25) ⇒1 + 50 = 51
Make x the subject: y = 4x - 3
y = 4x - 3
<u>+3 +3</u>
3 + y = 4x
<u>÷4 ÷4 </u>
(3+y)/4 = x
16.29cm hope that this maeks it better, i had to type atleast 20 cha9rwhrfhehf
I think the answer is 3x-y=11