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Differentiate arctan(x) with respect to x. Leave your answer in terms of x

Let y = arctan(x). Arctan(x) is difficult to differentiate but I know how to differentiate tan(x) (=sec^2(x)) so take the tan of both sides: tan(y) = x. The next step will be to differentiate both sides. To ...
BC
Answered by Benedict C. • Maths tutor
5306 Views

Differentiate with respect to x: 3 sin^2 x + sec 2x

6 sinx cosx + (2 sin 2x)/(cos^2 2x)
HM
Answered by Hugo M. • Maths tutor
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How do you solve a quadratic inequality eg find the values of x for which x^2 -6x +2 < -3

First we must change our inequality so that we have a zero on one side, In this case we can add three to both sides of the inequality, this gives: x^2 - 6x +5 &lt; 0 Now let's consider the equation y = x^2 -...
IR
Answered by Isobel R. • Maths tutor
4966 Views

2 equations intersect each other, y = x + 2 and y = x^2. Find the area of the shaded region between the points of intersection giving your answer to 3 significant figures. (shaded region will be shown)

points of intersection are (-1,1) and (2,4). Area of the shaded region is 4.5.
SA
Answered by Syed A. • Maths tutor
3545 Views

What is the differential of y =sin(2x)?

For this question we have to use the chain rule. The chain rule is dy/dx (the differential you are looking for) = du/dx (the differential of u with respect to x) * dy/du(the differential of y with respect to...
CU
Answered by Cem U. • Maths tutor
8008 Views