Why do we need to differentiate?
Differentiation is a very important tool for mathematicians. Although finding the gradient of a line can seem to lack a point, it does have some very important applications. For example, in mechanics the velocity of an object is equal to the differential of the displacement. It also allows the maximum or minimum of a line to be found, a highly useful tool in physics.
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Why is the derivative of inverse tan(x) 1/(1+x^2)?
For a curve of gradient dy/dx = (2/(x^2))-x/4, determine a) d^2y/dx^2 b) the stationary point where y=5/2 c) whether this is a maximum or minmum point and d) the equation of the curve
Find dy/dx in terms of t for the curve given by the parametric equations x = tan(t) , y = sec(t) for -pi/2<t<pi/2.