Top answers

Why is ꭍ2x=x^2+C?

Differentiating x 2 gives dx 2 /dx=2x. Differentiating a constant C gives 0. d( x 2 +C)/dx=dx 2 /dx+dC/dx=2x+0=2x. Since integration is the inverse function of differentiation, integrating 2x gives x 2 +C.
LD
Answered by Larisa D. • Maths tutor
6255 Views

Find the stationary points of the curve y (x)= 1/3x^3 - 5/2x^2 + 4x and classify them.

To find the stationary points of the curve y(x), you must first differentiate the equation for y(x) in terms of x. This gives d(y(x))/dx = x^2 -5x +4. Now set this differential equal to zero and solve for x ...
DR
Answered by Danny R. • Maths tutor
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Find the indefinite integral of x^8*ln(3x) using integration by parts

For this method we need to choose our u and dv/dx. Using the Late method (Logarithm, algebra, trigonometric, exponential), we can pick our u value which will be ln(3x). du/dx is therefore 1/x, using the chai...
JB
Answered by Joel B. • Maths tutor
6396 Views

A curve has an equation: (2x^2)*y +2x + 4y – cos(pi*y) = 17. Find dy/dx

You must differentiate each individual term in the equation.Firstly start with the term of the product of 2x 2 * y, using the product rule (dy/dx = u dv/dx + v du/dx)Let u = 2x 2 and v = yDu/dx = 4x and dv/d...
MB
Answered by Matthew B. • Maths tutor
4042 Views

A curve f(x,y) is defined by sin(3y)+3ye^(-2x)+2x^2 = 5. Find dy/dx

In questions where we have a function of x and y equal to a constant, we need to find dy/dx indirectly.We use the formula (df/dx) + (df/dy)(dy/dx) = 0So all we do is differentiate each term in the function w...
LW
Answered by Lewie W. • Maths tutor
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