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The  easiest way to see this is with an example. So let us take the curve:

    x = cos(2t) ,  y = sin(t) with a point P where t = pi/6

The grad...

There are two ways of multiplying vectors: one gives you another vector (cross product) and the other gives you a scalar- a number, like 3, 18 or 196 352. Hence, dot product is also called the scalar prod...

You can express tan(x) as sin(x)/cos(x). Therefore, tan(x)= sin(x)/ cos(x)The quotient rule can be applied here as there is a function of x in the numerator and denominator.Quotient Rule: (v*(du/dx) - u*(...

In differentiation you multiply the coefficient of the subject (what the value is multiplied by e.g. 3 is the coefficient of 3x⁶) by its exponent (the power that the value is raised to e.g. ...

This question is really straight forward

By using the Chain rule: f'(x) = uv' + u'v.

let u=3x, so u'=3

let v=(2x-1)^2, so v'=2x2(2x-1)=8x-4

Now, ...