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find dy/dx where y = a^x

First, we need to re-write it as e to the power something. The definition of log base e is that e^log(y) = y. We can put our expression into this equality too. So a^x = e^log(a^x), so we use log rules to bri...
AS
Answered by Alastair S. • Maths tutor
3553 Views

Derive the quadratic equation.

So in order to derive the quadratic equation we need to start with a quadratic that can represent any quadratic equation. Lets start with ax 2 +bx+c=0. We will use the completing the square method to solve t...
HT
Answered by Harry T. • Maths tutor
3960 Views

Find the gradient of y=x^2-6x-16 at the point where the curve crosses the x-axis

So we have y = 0 and therefore x 2 - 6x - 16 =0 This is then factorised to (x+2)(x-8) = 0 and therefore we have x = -2, x = -8 To find the gradient we need to find dy/dx So dy/dx = 2x - 6 Therefore if x = -2...
HK
Answered by Holly K. • Maths tutor
4818 Views

How do I know which trigonometric identity to use in any given situation?

For the most part, this comes down to practice. The insight in seeing which identity gives you the most efficient path to the solution comes with experience, however a little trick I like to use (silly as it...
AT
Answered by Ankush T. • Maths tutor
4056 Views

Find values of y such that: log2(11y–3)–log2(3) –2log2(y) = 1

NB.: Treat all log as log2 for purpose of formatting log(x) - log(z) = log(x/z) alog(b) = log(b^a) log((11y - 3)/3) - log(y^2) = 1 log((11y - 3)/3y^2) = 1 11y - 3 / 3y^2 = 2^1 11y - 3 = 6y^2 6y^2 - 11y + 3 =...
SA
Answered by Shrinivas A. • Maths tutor
6145 Views