3.14 x 81 = 254.34
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By the 'Chain Rule' dy/dx = dy/du X du/dx Y = Cos (pi*x). Let pi*x = u Y = Cos(u) u = pi*x dy/du = -Sin(u) du/dx = pi Hence dy/dx = dy/du X du/dx => ( Chain Rule) dy/dx = -Sin(u) X pi Substitute u for pi*x Hence dy/dx = -Sin(pi*x) X pi Tidying up dy/dx = -piSin(pix) Done!!!!
Can you please claify if you mean x=y^2/ pi*cos(x) , or x=y^2/cos(pi), since they are very different sums.
X = 81 sqrt(X) + 3 = 12 ( subtract 3 from each side ) sqrt(X) = 9 (square both sides ) X = 81 ( the square root of 81 is 9 )
81 x 4 equals 324. This can be calculated by multiplying 81 by 4, which is the same as adding 81 four times. In simpler terms, you can think of it as 81 multiplied by 4, resulting in the product of 324.
The method to use is 'integration by parts'; set u =x; du=dx; dv = sin(pi x)dx; v = cos(pi x)/pi. so integral(u dv) = u*v - integral(v du) then repeat the process.