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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 = 2u and du/dx = 3, so dy/dx = (2u)...
NB
Answered by Nishit B. • Maths tutor
10395 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 differentiate x...
OH
Answered by Oli H. • Maths tutor
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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+x 3 Differentiating with respect to x gives du/dx=3x 2 We now ha...
RM
Answered by Rebecca M. • Maths tutor
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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 of ...
EW
Answered by Edmond W. • Maths tutor
9337 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?

Recognise that the intial potential energy and kinetic energy at 10 m/s position should be identical due to the frictionless slope. mgh = 0.5mv 2 10kJ = 0.5 x m x 10 2 10 000 = 0.5 x m x 100 50m = 10 000 m =...
DM
Answered by Daniel M. • Maths tutor
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