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y=e^x When we derive, the power is brought down to the front - e.g. 2e^2x. Once this has been reached, you must normally remember to reduce the power by 1. However, with the exponentials, the power remain...

Rearrange to get x^2 - 9x - 36 <= 0 Solve quadratic (x-12)(x+3) <= 0 Solve for x x = 12, x = -3

Now, we have key points 12 and -3, we need the range of values for x where x^2 - 9x - 36 &...

This result comes from using a trig identity and the quotient rule. First, we write tan(x) as sin(x)/cos(x). Then we apply the quotient rule. After doing the standard derivatives, the numerator of our fra...

Use the product rule d(u.v)/dx = u.(dv/dx) + v(du/dx). Calculate the LHS as such first. (Demonstrate on whiteboard.) Then calculate the RHS. (Demonstrate on whiteboard.) Group the dy/dx terms on one side ...

When we find dy/dx we find the gradient of the curve at (3,1). Start by differentiating the left hand side (LHS) like so.. (whiteboard). Remember every time we differentiate a y value we multiply by dy/dx...