I am in calculus class right now and I have no idea. I'm sorry for my ignorance.
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$\begingroup$The derivative can be defined as the slope of a tangent line. When taking a derivative the general formula to follow would be:
- Constant Rule $\frac{d(c)}{dx}=0$
The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. In other words, it is the opposite of a derivative.
It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems
Example: The antiderivative of $\sec^2x = \tan x + C$
It is also important to remember, when taking the antiderivative, not to forget to add your constant!
$\endgroup$ $\begingroup$The anti-derivative of a function, denoted by $$\int f(x)dx$$ yields a function that when differentiated, gives back $f(x)$, while differentiating denoted by $$\frac{d}{dx}f(x)$$ yields a function for the slope of the tangent line at any given $x$ which youre probably used to by now.
$\endgroup$ $\begingroup$There is not only a difference between antiderivative but also a relation ship. Antiderivative is a "sort of inversve of the derivative" (note, this is not really true, just a somewhat intuitive description, which is the reason for quotations) in the sense of if $f=F'$ then $f$ is derivative of $F$ and $F$ is antiderivative of $f$. Antiderivative is often denoted as an integral, i.e. $F=\int f$ but there is examples of $\int f(x)dx = L$ where no $F(x)$ exists, for example see this link.
$\endgroup$ $\begingroup$Anti derivative is integration indefinite integration gives any equation relating $x,y$ while definite integration is area under the given curve while derivatives is finding the slope of given curve . Thats what the basic difference and definitions are. But i would also like to tell you never forget to write $+c$(constant) when you have found out the integration result as its very important. You will get it as you proceed further in calculus
$\endgroup$ 1 $\begingroup$Derivative is rate of change and it can also find the slope as well, in it you can find the piece wise change, while anti-derivative is synonimus to intergration which is inverse of derivatives, it is sometimes used to find the area under the curve, also to find the length of the curve $y=f(x)$
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