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Differentiate (x^2)cos(3x) with respect to x

First we start off by seeing that we are multiplying together two functions both containing x, so we want to apply the product rule. As we know the product rule is (f(x)g(x))'=f(x)g'(x)+f'(x)g(x) so we can a...
AB
Answered by Arthur B. • Maths tutor
9750 Views

Write (3 + 2√5)/(7 + 3√5) in the form a + b√5

First multiply top and bottom by conjugate of denominator, (7-3√5), and expand(3 + 2√5)(7 - 3√5)/(7 + 3√5)(7 - 3√5)(21 + 14√5 - 9√5 - 30)/(49 + 3√5 - 3√5 - 45)Simplify top and botton(-9 + 5√5)/4Write in requ...
BA
Answered by Beth A. • Maths tutor
6160 Views

Expand using binomial expansion (1+6x)^3

(1+6x)^3 = 1+3(6x) +(3)(2)(36x^2)/2 + (3)(2)(1)(216x^3)/6 = 1+18x+108x^2 + 216x^3
OO
Answered by Ola O. • Maths tutor
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Determine the next two terms in this sequence: 2, 7, 9, 16, 25, ... , ...

In this sequence, there is no common difference between one term and the next making it more challenging to solve. However, if you look at the terms closely, you can see that each term is the sum of the prev...
EW
Answered by Eleanor W. • Maths tutor
14034 Views

Find the gradient at the point (0, ln 2) on the curve with equation e^2y = 5 − e^−x

Question is asking for gradient at x = 0, y = ln2. e^2y = 5 - e^-x. Differentiation with respect to x: 2e^2y * dy/dx = e^-x . dy/dx = e^-x / 2e^2y. At x = 0, y = ln2 ~ dy/dx = e^0 / 2e^2ln2 = 1 / 2e^ln4 = 1 ...
LK
Answered by Lokmane K. • Maths tutor
5729 Views