What is differentiation and how do I do it?

explain the following briefly: To work out the gradient, first principles, shortcutsexplain in detail: different methods

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Find the equation of the tangent to the circle x^2 + y^2 + 10x + 2y + 13 = 0 at the point (-3, 2)


The line y = (a^2)x and the curve y = x(b − x)^2, where 0<a<b , intersect at the origin O and at points P and Q. Find the coordinates of P and Q, where P<Q, and sketch the line and the curve on the same axes. Find the tangent at the point P.


Expand and simplify (3 + 4*root5)(3 - 2*root5)


Chris claims that, “for any given value of x , the gradient of the curve y=2x^3 +6x^2 - 12x +3 is always greater than the gradient of the curve y=1+60x−6x^2” . Show that Chris is wrong by finding all the values of x for which his claim is not true.


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