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This is a common question asked by my students when they first learn about trigonometry. First draw a unit circle on the plane and the graphs of sine and cosine next to it. The circle obviously has 360 de...

First step is to understand all the notation, i.e. the prime for derivative. We then need to understand that the derivative is the gradient of the tangent at a point. In this case at the point P we can fi...

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))'...

I don't know how effectively I can communicate this answer via text without the whiteboard but I'll try.

i) First implicitly differentiate with respect to x: 2x + 2y * dy/dx = 0.

Rearranging...