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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 2xe^3...

Differentiating x² gives dx²/dx=2x. Differentiating a constant C gives 0. d( x² +C)/dx=dx²/dx+dC/dx=2x+0=2x. Since integration is the inverse function of differ...

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...

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 c...