Search over 10,000 free study notes

This type of question appears over-complicated with limited options, but one must not fear! At first, the numerator seems to be of a higher degree than the denominator (x^4 compared to x^2), but from the ...

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6xsin(2x). uv' = 6x^2cos(2x), v^2 = 4cos^2(2x) Therefore the differe...

Use the product rule: u'v + uv' u = 2x     V= sin3x u'= 2       v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x

Look at each of the x variables to determine what happens to each term.

3x^2 has a power of 2 on the variable, therefore, the 2 is multiplied by the coefficient on the x. You must also subtract 1 f...

We are being asked to find the rate of change of radius, dr/dt. We will need to use the chain rule to do this: dV/dt = dV/dr * dr/dt.

We are given that dV/dt is 10cm^3 per second, and differentiati...