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Work out the value of 5^3-5^2:

The first step would be to consider each of the powers individually, work out their value and then proceed with the subtraction to end up with a result. Firstly, as this question is to be done without a calc...
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Answered by Alexander B. • Maths tutor
13869 Views

Differentiate with respect to x: i) y=x^3ln(2x) ii) y=(x+sin(2x))^3

i) There first step is to acknowledge the need for both product rule (d(uv)/dx=v.du/dx+u.dv/dx) and chain rule (dz/dx=dz/dy*dy/dx). Here, u=x^3 and v=ln(2x). Therefore, du/dx=3x^2 which is a standard differe...
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Answered by Edward M. • Maths tutor
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Factorise and solve x^2-8x+15=0

Factorise means we want to turn x 2 -8x+15=0 into the form (x+a)(x+b)=0 . We need to find the two whole numbers 'a' and 'b' which equal -8 (from the -8x part) when added together, i.e. a+b=-8 , and equal 15 ...
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Answered by Anokhi C. • Maths tutor
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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...
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Answered by Sara R. • Maths tutor
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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...
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Answered by Aman G. • Maths tutor
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