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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. ...

Answered by Benedict C. • Maths tutor

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

6 sinx cosx + (2 sin 2x)/(cos^2 2x)

Answered by Hugo M. • Maths tutor

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The functions f and g are defined on R , the set of real numbers by f(x) = x^2 - 5x +2, and g(x) = 1 - x. Find h(x) = f(g(x)), and j(x) = g(f(x)).

Part 1: Step 1: Substitute in (1-x) for x in the equation f(x) = x^2 -5x +2 Step 2: Break the brackets Step 3: Collect like terms to simplify Part2: Step 1: Substitute in (x^2 -5x +2) for x in the equatio...

Answered by Daniel H. • 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 < 0 Now let's consider the equation y = x^...

Answered by Isobel R. • Maths tutor

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