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Find the gradient of the curve y = x^2(ln(x)) at x = e

We'll need to use the product rule. Let's take u = x^2 -> du/dx = 2x, and v = ln(x) -> dv/dx = 1/x Then dy/dx = x^2(1/x) + 2xln(x) = x + 2xln(x) Substituting our x value gives (dy/dx)|(x = e) = e + 2el...
CR
Answered by Charlie R. • Maths tutor
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5w -3 = 3w + 15

5w -3 = 3w + 15 Need to get the numbers on one side, and letters on the other side. 5w = 3w + 15 + 3 5w - 3w = 15 + 3 2w = 18 w = 18/2 w = 9
HN
Answered by Hannah N. • Maths tutor
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Explain why socialists support collectivism.

Socialists tend to support collectivism as they believe that both society and individuals benefit from a cooperative economic system. Socialists argue that humans are best able to fulfil their potential wher...
LP
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Using the substitution u=cosx + 1, show that the integral of sinx e^cosx+1 is equal to e(e-1), for the values of x between x=π/2 and x=0

First we differentiate the substitution giving, du/dx=-sinx, which is rearanged to dx=du/-sinx. we can then substitute this into the integral to get sinx e^cosx+1 du/-sinx which can be simplified to -e^cosx+...
KS
Answered by Kieran S. • Physics tutor
11797 Views

Are there any uses of animal imagery in John Steinbeck's 'Of Mice and Men'?

Most often applied to Lennie, imagery is particularly apparent in his physical description. His hands are called "paws" and indicate trouble when he uses them. He lumbers along like a bear in Stein...
TD
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