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How would I differentiate a function such as f(x)=x^3(e^(2x))?

Here, f(x)=x 3 e 2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(x)+u'(x)v(x). The firs...
LB
Answered by Lauren B. • Maths tutor
3916 Views

Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the frac...
OG
Answered by Omar G. • Maths tutor
7291 Views

How do you find (and simplify) an expression, in terms of n, for the sum of the first n terms of the series 5 + 8 + 11 + 14 + ... ?

Normally, this would be quite hard! We'd have to play around with the sequence and try different formulas until something worked. Luckily, this is what we call an "Arithmetic Series". That's becaus...
MS
Answered by Matthew S. • Maths tutor
19683 Views

How do you find the maximum and minimum value of a quadratic function with no use of calculus?

By completing the square, since this makes you see that the square will always be >= 0 and the other part allows you to calculate the minima or maxima depending on the sign in front of x 2 . E.g. x 2 +4x=...
AO
Answered by Alexander O. • Maths tutor
10430 Views

Sunita has 75 pens and she ties them into bundles of 8. How many pens does she have left over?

We can work the remainder by using division, and one of the most common methods to use is long division. (Here I would present the method on a whiteboard) As we can see, the closest multiple of 8 to 75 is 72...
MU
Answered by Melanie U. • Maths tutor
4093 Views