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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
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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
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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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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
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1. (a) Find the sum of all the integers between 1 and 1000 which are divisible by 7. (b) Hence, or otherwise, evaluate the sum of (7r+2) from r=1 to r=142

1a) 1000/7=142.8.... Therefore there are 142 multiples of 7 between 1 and 1000 Therefore the sum of series from 1 to 142 is 1/7th of the solution Calculation:7 0.5 142 143=71071 1b) The sum of (7r+2) from r=...
JF
Answered by Jack F. • Maths tutor
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