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Stationary points occur when the gradient of the function is zero. They can be visualised on a graph as hills (maximum points), as troughs (minimum points), or as points of inflection. (I would draw all t...

This a relatively simple question which requires the use of the chain rule to solve. First we set u = sin(x)  so we then have y = u² . Next we perform do differentiations, one on u as a functio...

To solve this problem, you need to: rearrange the first equation (1) to express y in terms of x to obtain equation (3). Then, substitute this new equation into the quadratic one (the second equation from ...

Using trig formulas we have sin(5x+3x)= sin(5x)cos(3x)+cos(5x)sin(3x) and sin(5x-3x)= sin(5x)cos(3x) - cos(5x)sin(3x). Hence, sin(5x+3x) - sin(5x-3x) = sin(8x)-sin(2x) = 2cos(5x)sin(3x). This implies that...

ln((4^x)e^(7x+5)) = ln21; apply a natural log on both sides of the equation as an exponential containing e is involved 

ln4^x + ln(e^(7x+5)) = ln21; using logarithm rules you can seperate the singl...