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What is the derivative of ln(x)?

First let y=ln(x). Recall that the exponential function, e x , is defined as the inverse of the logarithmic function, ln(x). To make x the subject of the formula, use the inverse function exp. This gives tha...
BG
Answered by Benjamin G. • Maths tutor
11852 Views

Why is it that sin^2(x) + cos^2(x) = 1?

Let's start with the definition of sin( x ) and cos( x ). We're going to use t rather than x here to avoid confusion, but the idea is exactly the same. Take a unit circle - that is, a circle with centre (0,0...
JT
Answered by John T. • Maths tutor
7667 Views

Prove that 0.565656.... can be expressed as 56/99.

1) Let x=0.565656... 2) Thus 100x=56.565656... 3) Subtracting equation 1) from 2) gives: 99x=56 4) Rearrange for x: x=56/99, Also x=0.565656... from 1) Therefore 0.565656...=56/99
DC
Answered by Daanyaal C. • Maths tutor
4695 Views

How can I move up in my AO2 bands in my History EPQ (AQA)?

Hi there! Your AO2 bands are about how you use evidence in relation to your argument. These are just a few tips about how you can improve. AO2 - 7-10 marks "Evidence of detailed research involving the s...
SD
12187 Views

How do you use the gerund in Latin?

The use of the gerund can be one of the most confusing aspects of Latin grammar. However, its use can be distilled into a relatively simple explanation. What is the gerund? Gramatically speaking, the gerund ...
TP
Answered by Toby P. • Latin tutor
11367 Views