query: Why is the circumference of a circle the derivative of the area of the circle?
positive_passages.docid: 5086
positive_passages.text: Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
negative_passages.docid: 123911
negative_passages.text: Why is the derivative of a vector orthogonal to the vector itself?
negative_passages.docid: 134871
negative_passages.text: Using definition of derivative to differentiate $f(x)= \sqrt{x}+1$
negative_passages.docid: 133580
negative_passages.text: Nth derivative of $x^x$
negative_passages.docid: 61144
negative_passages.text: Derivative of $x^{x^{\cdot^{\cdot}}}$?
negative_passages.docid: 28890
negative_passages.text: Why does the tangent of numbers very close to $\frac{\pi}{2}$ resemble the number of degrees in a radian?
negative_passages.docid: 88854
negative_passages.text: Simple way to understand what derivative is
negative_passages.docid: 98971
negative_passages.text: Why is $\pi r^2$ the surface of a circle
negative_passages.docid: 153794
negative_passages.text: What is the meaning of $1/(D+a)$, where $D$ is the derivative operator?
negative_passages.docid: 71861
negative_passages.text: Circles and tangents and circumcircles
negative_passages.docid: 152111
negative_passages.text: Difference between differentiation and derivatives
negative_passages.docid: 151864
negative_passages.text: Derivative of the Absolute Value Function in Mathematica looks very different from the actual answer
negative_passages.docid: 65491
negative_passages.text: if the curvature is constant and positive, then it is on the circunference
negative_passages.docid: 115677
negative_passages.text: Prove the equality of circle's areas
negative_passages.docid: 3948
negative_passages.text: Why do we require radians in calculus?
negative_passages.docid: 152853
negative_passages.text: What is the intuition behind the unit normal vector being the derivative of the unit tangent vector?
negative_passages.docid: 73867
negative_passages.text: Radius of circumscribed circle of triangle as function of the sides