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Differentiate (3x)e^(3x)

3e^3x + (9x)e^3x This is a good question because it involves the use of both the chain and product rules of differentiation, as well as the differential of e (all of which occur frequently in Maths A-level a...
JH
Answered by Joe H. • Maths tutor
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The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a, and the common difference, d, of the sequence.

Let a be the first term Let d be the common difference a + d = 7 S 4 = 4/2 (2a +3d) = 12 Simultaneous equation: a+d =7 // x 6 4a +6d = 12 Difference btween these two 6a + 6d = 42 4a +6d = 12 2a = 30 a = 15 d...
AT
Answered by Alexander T. • Maths tutor
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Integrate 5cos(3x - 1) with respect to x

Firstly, we may simplify the expression by factoring out any constants. In this case 5 can be factored out. 5 ∫ cos(3x-1) dx For the integrand cos(3x -1), we can use a simple u-substitution. Where u = 3x -1 ...
RM
Answered by Rian M. • Maths tutor
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Solve the equation x^2-x-56=0

The first step in this solution is to factorise the equation we have been given into the form (ax+b)(cx+d)=0, where a, b, c and d are constants which we need to determine. If we were to expand the brackets w...
RC
Answered by Richard C. • Maths tutor
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(3 + root(a))(4 + root(a)) = 17 + k(root(a)) where a and k are positive integers. Find the value of a and the value of k.

Let's open out the bracket using the FOIL method (first, outside, inside, last): (3 + root(a))(4 + root(a)) = 12 + 3root(a) + 4root(a) + (root(a)) 2 = 12 + 7root(a) + a. Since the answer 17 + k(root(a)) is i...
AJ
Answered by Abhinav J. • Maths tutor
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