Question

Find%3D%203%20%7Bx%20%7D%5E%7B2%7D%20%20%2B%20y" id="TexFormula1" title="find \frac{dy}{dx} of \: the \: equation \: y = 3 {x }^{2} + y" alt="find \frac{dy}{dx} of \: the \: equation \: y = 3 {x }^{2} + y" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

dy/dx does not exist.

Step-by-step explanation:

If a question asks us to find dy/dx of a equation, it is asking us to find the derivative of a function.

There are two main ways to find the derivative of a function:

• Use definition ($\mathop {\lim }\limits_{h\to0}\frac{{f\left({x+h}\right)-f\left( x\right)}}{h}$)
• Use derivative rules (product rule, quotient rule, power rule, exponential rule, etc...)

Something important to remember when finding the derivative of a function:

• If the equation is in the form g(x) = c (such as x = 1, x² = 5, √x = 4, etc...), where c is a constant, the derivative does not exist. This makes sense, since the derivative of a function is an equation for the slope of a function, and the slope of a function in the form g(x) = c has an undefined slope.

We are given the function y = 3x² + y, and we are asked to find dy/dx. See how the y's on each side cancel out:

y = 3x² + y

-y           -y

0 = 3x²

This is in the form g(x) = c, where c = 0 and g(x) = 3x². There is no derivative to this function. Therefore, dy/dx does not exist.

I hope this helps. :)