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A derivative, in essence, is the gradient of a function at a point, usually denoted by dy/dx, or f'(x). It essentially means the rate of change of y with respect to x. As many functions are complex, we can n...

Expand and simplify ( n + 2) 3 − n 3 . Write out the brackets in full:( n + 2)( n + 2)( n + 2) − n 3 Use F.O.I.L. (First, Outer, Inner, Last) on first two sets of brackets:( n 2 + 2 n + 2 n + 4)( n + 2) - n ...

Looking at the first element of the equation 5x 6 , we can simply multiply 6 by 5 to give 30 and subtract 1 from the power of x. So d/dx[5x 6 ] = 30x 5 . The next element of the equation is 4x sin(x 2 ), whe...

Using log rules, we can simplify the equation as follows: Firstly log(x a ) = a log(x) implies that ln(e 2 ) = 2 ln(e). Next log a (a) = 1 implies 2 ln(e) = 2 1 = 2 [Since the natural logarithm ln is equival...

If you have a plot of the function, you can look at its symmetries. If the plot to the left of the y axis is the mirror image with respect to the y axis of the plot to the right, it's an even function. If th...