Top answers

Differentiate f(x) = (x+3)/(2x-5) using the quotient rule.

For a quotient f(x) = u(x)/v(x), the derivative is f'(x) = (v u'(x) - u v'(x))/v(x) 2 . Applying this to the given function, we find u(x) = x+3 and v(x) = 2x-5. So, u'(x) = 1 and v'(x) = 2. We can then put t...
SR
Answered by Sara R. • Maths tutor
6467 Views

The first four terms of an arithmetic sequence are : 11, 17, 23, 29. In terms of n, find an expression for the nth term of this sequence.

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. We can work this out for the sequence 11, 17, 23, 29. To go from the 1st term (11) to the 2...
AG
Answered by Aman G. • Maths tutor
18929 Views

Integrate 2x/(x^2+3) using the substitution u=x^2+3

u=x 2 + 3 du/dx=2x dx=du/2x 2x/(x 2 +3) dx becomes (2x/u) * (du/2x) the 2x terms cancel out giving 1/u du this integrates to ln(u)+c becoming ln(x 2 +3)+c
TS
Answered by Tom S. • Maths tutor
14911 Views

Core 1: Given that y = x^4 + x^2+3. Find dy/dx

First what we need to do is we need to think of what the question is asking us to find. In this case it is dy/dx but what is this. This is the rate of change of y with respect to x. For understanding purpose...
DS
Answered by David S. • Maths tutor
3512 Views

Write x^2 + 8x + 7 in the form (x + a)^2 + b

We work from right to left (x + a) 2 = x 2 + 2ax + a 2 2a = 8 [coefficients of x must match] a = 4 (x + 4) 2 = x 2 + 8x + 16 [substitute in a = 4] x 2 + 8x + 16 + b = x 2 + 8x + 7 [equate sides and solve for...
WM
Answered by Will M. • Maths tutor
14766 Views