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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...

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 ...

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...

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/d...

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 o...