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Differentiate x^x

(x^x)(ln(x)+1)
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Answered by Aadil V. • Maths tutor
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Using substitution, integrate x(2 + x))^1/2 where u^2 = 2 + x

u 2 = 2 + xx = u 2 - 2dx/du = 2u ʃ x(2 + x)) 1/2 dx= ʃ xu dx= ʃ u(u 2 - 2) dx= ʃ 2u 2 (u 2 - 2) du= ʃ 2u 4 - 4u 2 du= [2/5u 5 - 4/3u 3 + C]= 2/5 (2 + x) 5/2 - 4/3 (2 + x) 3/2 + C
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Answered by Sonali P. • Maths tutor
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Please explain (said question) surrounding a proof of 2 equal angles

I would firstly ask them how much they knew about trigonometry, and then guide them through the SoHCaHToA theory. I would use diagrams for this. I would then ask them to spot any ways they could work out any...
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Answered by Kate P. • Maths tutor
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The volume, V, of water in a tank at time t seconds is given by V = 1/3*t^6 - 2*t^4 + 3*t^2, for t=>0. (i) Find dV/dt

The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. x a ...
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Answered by Samuel W. • Maths tutor
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I don't understand Pythagoras' theorem . What is it and how do you use it?

Ok, so the reason we need the Pythagoras theorem is to work out the length of missing side given we know the other 2 sides in a right-angled triangle. (Would go on to draw the triangle with the known sides a...
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Answered by Stefano M. • Maths tutor
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