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The product rule states that if y=uv, where u and v are both functions of x , then dy/dx = u(dv/dx) + v(du/dx) Therefore, the differential of 2x e 3x can be found by letting 2x= u and e 3x =v . u= 2x, du/dx ...

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.

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 ...

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...

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...