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i) For this question we need to use the product rule as there are two functions that are being multiplied together Product Rule: (uv)'=u'v + v'uApply this formula to the problem: xcos2x =...

Write i in terms of an exponential, so i = e^(i pi/2).Then the three roots of i are:z_1 = [e^(i pi/2)]^(1/3) = e^(i pi/6) = sqrt(3)/2 + i/2z_2 = e^[i (pi/6 + 2pi/3)] = e^(i 5pi/6) = -sqrt(3)/2 + i/2z_3 = ...

What does derivative mean? The derivative of a function the represents the gradient of the function for each value of x. Remark that the gradient of a function at point (x,f(x)) is equal to the gradient o...

Being a quadratic equation in the following form,the simplest way to solve would be through the quadratic formula which goes as follows:
The first step to solving is therefore to identify a, b, c, wi...

f(x) = 7xe^xUsing the product rule: [f'(x)=u*(dv/dx)+ v*(du/dx)]Let u=7x and v=e^xTherefore, du/dx=7 and dv/dx=e^xHence, f'(x) = 7xe^x + 7e^x