The _____________ of a function is a formula for the slope of the tangent line to that function at any point x.
When the function is defined as f(x), the derivative will be written as __________or ________. When the function is written in the form of y =, the derivative is written as ________ or ______________.
Can you help with the blanks.
I think the first one is derivative.
And I think the other two are y' or f'(x).
And Im not sure about the last ones..
#1 correct
#2 is only partially complete
f'(x) or df/dx
y' or dy/dx
f'(x) or d f(x)/dx
y' or dy/dx maybe?
You are correct! The first blank is indeed filled with "derivative."
For the second blank, when the function is defined as f(x), the derivative can be denoted as either "f'(x)" or "dy/dx". Both of these notations represent the derivative of the function with respect to x.
For the third blank, when the function is written in the form of "y =", the derivative is written as "dy/dx" or "y'". These notations indicate the derivative of y with respect to x.
To summarize, the derivatives can be denoted as:
- When f(x) is the function: f'(x) or dy/dx
- When the function is in the form of "y =": dy/dx or y'