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Maths
A Level

If y = (1+3x)^2, what is dy/dx?

A good approach to solve this is to use the chain rule of differentiation. The chain rule states: dy/dx= (dy/du)*(du/dx).

In this case let u = 1+3x, so y = u^2.

Then dy/du =...

Answered by Nishit B. Maths tutor
8376 Views

How would you differentiate ln(x^2+3x+5)?

Here we need to use the chain rule because we have a function (natural log) of another function (x^2+3x+5). Let u=x^2+3x+5, and differentiate lnu with respect to u, this gives us 1/u. Then we different...

Answered by Oli H. Maths tutor
22426 Views

Given y=(1+x^3)^0.5, find dy/dx.

In order to solve this question, we need to use the chain rule when differentiating. The chain rule formula is dy/dx= (dy/du)(du/dx). Let u=1+x3Differentiating with respect to x gives du/dx...

Answered by Rebecca M. Maths tutor
5089 Views

At t seconds, the temp. of the water is θ°C. The rate of increase of the temp. of the water at any time t is modelled by the D.E. dθ/dt=λ(120-θ), θ<=100 where λ is a pos. const. Given θ=20 at t=0, solve this D.E. to show that θ=120-100e^(-λt)

When solving any differential equation, the first method to consider is the seperation of variables. This is the simplest method and, conveniently, it works in this case. To seperate variables:1. Put all ...

Answered by Edmond W. Maths tutor
7846 Views

A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

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