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dx/dt = -5x/2 to solve this we must firstly separate the variables ∫2/x dx = -∫5 dt then we solve the integrals using basic integration formulae 2ln...
integrate using substitution: (I = the symbol for integration)let u = 2x + 5 therefore x = (u - 5)/2 du/dx = 2 which means that du = 2dx ---> dx = 1/2 duThis means that the integral now = I((u - 5)/2 x...
using the quotent ruledy/dx= (3(x^2+6)-3x(2x))/(x^2+6)^2dy/dx=3(x^2+6-2x^2)/(x^2+6)^2dy/dx=(18-3x^2)/(x^2+6)^2
To find dy/dx, we must use a combination of the Product Rule and the Chain Rule.If we let 3x^2=u and (x+2)^6=v, the Product Rule tells us that (uv)' = uv'+vu'u'=6x, but to find v' we need to u...
A matrix is a linear transformation between vector spaces. Often we want to think about linear maps from an n-dimensional vector space to itself. When the vector space that we're mapping to and f...
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