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Differentiate ln(x^3 +2) with respect to x

The differential of ln(x) is x^-1 or 1/x. Because we have x^3 + 2 inside the bracket we have to differentiate this term also and multiply this with the other term. For example, d/dx of x^3 +2 is equal to 3x^...
GL
Answered by George L. • Maths tutor
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A curve is defined by the parametric equations: X = 3 – 4t , y = 1 + (2/t) Find (dy/dx) in terms of t.

When dividing fractions by fractions with a common factor: (a/c) / (b/c) = (a/c) * (c/b) = (ac/bc) we can cancel the common factor to get (a/b). So in this question we can do the same: (dy/dt) / (dx/dt) = (d...
EE
Answered by Eddie E. • Maths tutor
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How would you work out the price of a trip if it is usually £24 but a man has a railcard that gives him 30% off?

In order to work out 30% off something you can use two methods. I'll explain both. Method one: Work out 30% of the total price. This would be the same as working out 10% (dividing by 10 = £2.40) and multiply...
CT
Answered by Chloe T. • Maths tutor
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How do I show (2n)! >= 2^n((n!)^2) for every n>=0 by induction?

First we need to be clear how to construct a proof by induction. It has two main parts, the base case and the inductive step . Let P(n) denote that the statement is true for a fixed n. Our base case is to ch...
CF
Answered by Connor F. • Maths tutor
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integrate cos(2x) + sin(3x)

the differential of cos(x) is -sin(x). the differential of cos(2x) is -2sin(2x). you can think of it as differentiating what is in the bracket and putting that in front of the -sin(2x). when differentiating ...
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Answered by Ajay D. • Maths tutor
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