124 results for "derivative".

Visualisation of limit definition of derivative
JSXGraph code based on original by Christian LawsonPerfect
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Diff: Quotient rule  differentiate exponential over exponential
The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.
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Diff: Quotient rule  differentiate linear over square root
The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.
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Diff: Quotient rule  differentiate quadratic over quadratic
The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.
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Andreas's copy of MA100 MT Week 9
This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.
Description of variables for part b:
For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:
a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying
Function 1: x^2 + ax + b sin(cx)
Function 2: x^2 + dx + f sin(gx)
Function 3: x^2 + hx + j sin(kx)
Function 4: x^2 + lx + m sin(nx)
u,v,w,r are variables satifying
u=a+bc
v=d+fg
w=h+jk
r=l+mn
The derivatives of each function, evaluated at zero, are:
Function 1: u
Function 2: v
Function 3: w
Function 4: r
So we will define
u as random(5..5 except(0))
v as u
w as 0
r as random(5..5 except(0) except(u) except(u))
Then the derivative of function 3, evaluated at 0, gives 0. The other functions give nonzero.
Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.We now take b,c,f,g,j,k,m,n to be defined as \random(3..3 except(0)).
We then define a,d,h,l to satisfy
u=a+bc
v=d+fg
w=h+jk
r=l+mnDescription for variables of part e:
Please look at the description of each variable for part e in the variables section, first.
As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:both: v1,v2,v3
span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
lin ind: v1+v2+v3
neither: v2+v3 , 2*v2 + 2*v3
neither:v1+v3,v12*v3,2*v1v3
neither: v1+v2,v1v2,v12*v2,2*v1v2Question Draft
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Last modified 11/09/2019 07:45
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Min_max_v1
Calculate the local extrema of a function ${f(x) = e^{x/C1}(C2sin(x)C3cos(x))}$
The graph of f(x) has to be identified.
The first derivative of f(x) has to be calculated.
The min max points have to be identified using the graph and/or calculated using the first derivative method. Requires solving trigonometric equation
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Last modified 16/08/2019 14:46
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Finding Derivative From a Graph
A graph is drawn. A student is to identify the derivative of this graph from four other graphs.
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Last modified 06/08/2019 08:11
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Differentiation 1  Basic Polynomial Expressions (with second derivatives)
A basic introduction to differentiation
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Last modified 11/07/2019 06:55
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Find the value from the derivatives
Given the derivatives of a cubic function at a point, find the value of the function at another point.
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Last modified 11/07/2019 05:20
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Mystery derivatives
Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.
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Last modified 11/07/2019 05:15
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