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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...

Let's first go to the whiteboard where I will explain what a logarithm is. The equation, loga(b) = x, could be re-written into the form, a^x = b. This is true for all logarithmic equations. There is a rul...

Differentiate the curve to get the gradient function: f'(x)= 2x + 5. Solve for x when f'(x) = 0 --> 2x + 5 = 0, 2x = -5, x = -5/2 Substitute into the original equation to find y: (-2.5)^2 + 5 * -2.5 + ...

Here, we have to use implicit differentiation, along with the product rule. Remember that the product rule is (vu)' = vu'+uv'. Moving through the equation we have: x^2+2xy+3y^2 = 4 ==> 2x +2y + 2x*(d...