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First we subtract ln(2-y) from both sides to get "ln(4y+7) - ln(2-y) = 3". By applying the laws of logs from C2, we have "ln[(4y+7)/(2-y)] = 3". Therefore, if we put them as exponents ...
Firstly I would state the substitution rule, letting 5xCos(3x)=w(x), and differentiating with respect to w(x). This gives y'(x)=2w'(x)(w(x)).I would then demonstrate the product rule stating ...
You first calculate the delta of the equation: delta = b^2-4ac = 16 - 16 = 0 => the solution is double.x1,2 = (-b±sqrt(delta))/2/a = 4/2/4 = 1/2 which is real.so the solutions are 1/2 and 1/2....
If a quadractic equation ax^2 + bx + c = 0 has no real solutions, this means that the discriminant is less than 0, i.e. b^2-4ac<0. Let's put our equation in this form: x^2 + kx + 8 = k rearranges to x^...
This is an example of implicit differentiation where we have to consider both the y-terms as well as the x-terms. The first step is to deal with each term on the left hand side individually. This gives us...
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