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Given y=x^2(1+4x)^0.5, show that dy/dx=2x(5x+1)/((1+4x)^0.5)

You have to differentiate the equation y=x^2(1+4x)^0.5 with respect to x to get dy/dx and thereby prove the result in the question. An equation composed of the product of two x terms can be differentiated wi...
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Answered by Alistair G. • Maths tutor
5724 Views

How do you solve inequalities when they involve quadratics? i.e x^2+x-6<0

It is easiest to first solve the quadratic as if it isn't an inequality. This will then help us to sketch the graph of the function which will in turn help us to solve the inequality. So let's change the &lt...
JM
Answered by Jake M. • Maths tutor
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expand the brackets: (x+3)(x+2)

(x+3)(x+2)we need to multiply each term by both terms in the other bracketFOIL helps us remember the process. First, Outer, Inner, Last so we don't forget any of them.Fist - in this case multiply the first x...
LW
Answered by Luke W. • Maths tutor
6357 Views

Expand the following (x+4)(x+2)

The most important thing to remember when expanding brackets is to make sure that all terms in the one brackets have been multiplied with all the terms in the other.In this case we have two terms in each bra...
JG
Answered by James G. • Maths tutor
5040 Views

Differentiate 2e^(3x^2+6x)

Subsitute in u = 3x^2 + 6x and use chain rule to get dy/dx = dx/du x dy/dx to get dy/dx = 2(6x+6)e^(3x^2 +6)
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Answered by Nasser C. • Maths tutor
4486 Views