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How do you differentiate x^x?

To differentiate x x , we first let y = x x . ( Note that x x is not in the form x c where c is a constant or a x where a is a constant so the usual differentiation formulas cannot be used ). The trick here ...
AP
Answered by Anish P. • Maths tutor
3870 Views

The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px^2 – 6px + 4p, where p is a constant. Show that 4p^2 – 20p + 9 < 0.

The main piece of information this question gives us is that the two lines do not cross or touch. From this we can immediately see that we will need to use the discriminant of the quadratic formula b 2 - 4ac...
MW
Answered by Molly W. • Maths tutor
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Let f(x) = 2x^3 + x^2 - 5x + c. Given that f(1) = 0 find the values of c.

In order to solve this question we simply must substitute x=1 into f(x). If we carry out this substitution we see that f(1) = 2(1^3) + (1^3) -5(1) + c = 2(1) + (1) -5(1) + c = 2 + 1 - 5 + c = 3 - 5 + c = c -...
CL
Answered by Calum L. • Maths tutor
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sin(x)/(cos(x)+1) + cos(x)/(sin(x)+1) = 1

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1 (sin^2(x) + cos^2(x) =1) Therefore; 1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1 Cancelling out on both sides cos(x)sin(x) =...
JO
Answered by James O. • Maths tutor
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What is the indefinite integral of cos^2x?

List Trigonmetric identities which could help to simpilfy integral Use cos(2x)= Cos 2 x-sin 2 x and sin 2 x=1-cos 2 x Sub identity 2 into 1 and rearrange to show Cos 2 x=(1+cos2x)/2 and integrate to find the...
JM
Answered by Jake M. • Maths tutor
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