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Supposing y = arcsin(x), find dy/dx

Suppose: y = arcsin(x) Then, x = sin(y) And, dx/dy = cos(y) ----- (1) Using: dy/dx = 1/(dx/dy); Thus 1 becomes: dy/dx = 1/cos(y) ------ (2) Using: sin^2(y) + cos^2(y) = 1; We can rearrange 2 to: dy/dx = 1/sq...
JN
Answered by James N. • Maths tutor
7424 Views

Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1

First differentiating by the rule that x n differentiates to nx n-1 we have that dy/dx = 4x 2 +6x-4. At the turning points of a curve the differential is equal to 0 so we set 0=dy/dx = 4x 2 +6x-4, by factori...
TE
Answered by Theo E. • Maths tutor
9534 Views

integrate xcosx

use integration by parts
SB
Answered by Sebastian B. • Maths tutor
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Find the minimum and maximum points of the graph y = x^3 - 4x^2 + 4x +3 in the range 0<=x <= 5.

First, use the standard method of setting the derivative to be equal to 0 to find the stationary points. This yields the equation 3x^2 - 8x + 4 = 0 and so the stationary points are at x = 2/3 and 2 respectiv...
GM
Answered by Guy M. • Maths tutor
6339 Views

A curve has equation x = (y+5)ln(2y-7); (i) Find dx/dy in terms of y; (ii) Find the gradient of the curve where it crosses the y-axis.

(i) To find the derivative we will use the product rule. Let u = y+5 and v=ln(2y-7). Then dx/dy = du/dy v + u dv/dy = ln(2y-7) + (y+5)*2/2y-7 (used the chain rule in 2nd term - can explain this on white boar...
SP
Answered by Szymon P. • Maths tutor
11770 Views