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Why do I need to add the + C when finding an indefinite integral?

When you differenciate a function, the constant term turns to 0. So a lot of different functions like x 2 + 7 and x 2 - 3 will have the same derivative, this means that going from the derivative to the origi...
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Given y = 3x^(1/2) - 6x + 4, x > 0. 1) Find the integral of y with respect to x, simplifying each term. 2) Differentiate the equation for y with respect to x.

When integrating remember the general rule: x^n --> x^(n+1)/(n+1). Now look at each term separately. 3x^(1/2) --> 3x^(3/2)/(3/2) = 2x^(3/2)-6x --> -6x^(2)/2 = -3x^24 = 4x^(0) --> 4x^(1)/1 = 4xCom...
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Answered by Scott O. • Maths tutor
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solve the differential equation dy/dx=(3x*exp(4y))/(7+(2x^(2))^(2) when y = 0, x = 2

Move y terms to the left hand side and the keep the x terms on the right hand side: dy*(1/(exp(4y))) = dx*(3x/(7+2x^(2))^(2)) First, solve the right hand side by using a substition: u = 7 + 2 x^(2), du/dx=4x...
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Differentiate the equation 4x^5 + 2x^3 - x + 2

When you differentiate you find the equation which lets you find the gradient of the equation at a specific point.To do so you multiply the power of the x by the respective coefficient, then that becomes the...
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What is the derrivative (dy/dx) of the equation 2 = cos 4x - cos 2y in terms of x and y?

A common C4 question where the student would need to use implicit differentiation to obtain an equation with the derrivative in it. 0 = -4sin4x + 2(dy/dx)sin2y. Then all that is required is rearranging the e...
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Answered by Arsh Y. • Maths tutor
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