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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...

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 ...

(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 firs...

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 ...

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)