Please explain the antiderivative Can someone please explain what an antiderivative

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f(x,y)=x^3-6xy+8y^3$

$\frac{1}{\sec <!--\; \; -->(x)}$ in derivative?

What is the derivative of ${\displaystyle \ln (x+1)}$?

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What is the derivative of ${\displaystyle f\left(x\right)=5^{\ln x}}$?

What is the derivative of ${\displaystyle e^{-2x}}$?

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What is the derivative of ${\displaystyle f\left(x\right)=\ln \left[x^9{(x+3)}^6{(x^2+7)}^5\right]}$ ?

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What is the antiderivative of ${\displaystyle -5e^{x-1}}$?

How to evaluate: indefinite integral ${\displaystyle \frac{1+x}{1+x^2}dx}$?