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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 =...

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...

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

First we should be aware of the relationship bewteen the denominator of the two fractions. Since x^2-9=(x+3)(x-3), we can multiply (x-3) on both numerator and denominator of the fraction of 2/(x+3). Henc...

To find the answer first you have to take a log of both sides.

I am going to use log to the base 2 for my example - but any base will work as long as they are the same on both sides of the equals s...