Top answers

Calculate the derivative of x^x

This problem is best solved using implicit differentiation and by tackling each side of the equation individually. First write down the problem as "y = x^x". Recalling that log rules can be used to...
GH
Answered by George H. • Maths tutor
4192 Views

How do you integrate sin^2(3x)cos^3(3x) dx?

Use the identity sin^2(y) + cos^2(y) = 1 to get the expression sin^2(3x) (1-sin^2(3x)) cos(3x) dx.Use the substitution u= sin(3x) by dividing the expression by the derivative, u’= 3cos(3x).The expression the...
ZG
Answered by Zachary G. • Maths tutor
9837 Views

two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u

ball A has mass m and velocity u. ball B has mass 2 m and velocity 2uby conservation of momentum:mu - 4mu = mv + 2mx (1)where v is the velocity of ball A and x is the velocity of ball B after collision.by co...
WA
Answered by William A. • Maths tutor
3837 Views

Find, using calculus, the x coordinate of the turning point of the curve with equation y=e^3x cos 4

1st step: find the derivative dy/dx of the given equation2nd step: now equate the obtained derivative to 0 because this is precisely the situation in which the graph changes direction (the derivative dy/dx e...
UW
Answered by Urszula W. • Maths tutor
4606 Views

How can I recognise when to use a particular method for finding an integral?

Often the question will ask you to use a particular method to integrate something, but sometimes they will not and you will have to recognise for yourself the best way to do it. There is often more than one ...
LC
Answered by Lloyd C. • Maths tutor
4295 Views