Question

Given x^3 square root of 4y is equal to 5.

Answer 1

The value of the square root function after differentiation is  $\frac{dy}{dx}= \frac{3}{x}$ .

The given equation is :

x³√4y = 5

Now we will use implicit differentiation

$\implies3x^2\sqrt{4y} \ \ dx +x^3\times 2(-\frac{1}{\sqrt y}) =0\\\\\implies6x^2\sqrt{y}\ dx-2\frac{x^3}{\sqrt y}\ dy=0\\\\\implies \frac{dy}{dx}= \frac{3}{x}$

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  $\frac{dy}{dx}= \frac{3}{x}$

to learn more about square root visit:

brainly.com/question/15208820

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