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 ([tex]\mathop {\lim }\limits_{h\to0}\frac{{f\left({x+h}\right)-f\left( x\right)}}{h}[/tex])
- 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. :)
