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In order to differentiate a trig function with a term in front of the variable you are differentiating, you must use the chain rule. For example d/dx (sin (3x)) becomes 3cos(3x) because you have to multip...

De Moivres theorem states that e^j(theta) = cos (theta) +jsin (theta) and this can be used to convert powered trig functions to the form of regular sines and cosines (i.e. sin^3(x) into a sum of terms inc...

The product rule states that (uv)' = u'v + uv' Therefore we know that to find dy/dx we must have (sin(2x))'(4x+1)^3 +sin(2x)((4x+1)^3)' We can differentiate sin(2x) to 2cos(2x) and using the chain rule we...

First, you have to understand that both are essentially the same; the formula is based on the completing the square method. ax^2+b^x+c=0 can with appropriate steps be transformed to x = (-b +- root(b^2-4a...

If a denominator is has just one square root (i.e 1/(3)^0.5). Then, since it is a fraction you can multiply top and bottom by the same number and maintain the value of the fraction. Hence we multiply top ...