126 results for "derivative".

Question in All questions
Q1 is true/false question covering some core facts, notation and basic examples. Q2 has two functions for which second derivative needs to be determined.

Question in All questions
A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four such questions.

Question in Blathnaid's workspace
A basic introduction to differentiation

Question in Archive
Antiderivatives
rebel
rebelmaths

Question in Maths supportCalculate d2y/dx2 for a curve defined parametrically

Question in MATH6006 20192020Differentiation by rule question with feedback given for anticipated student errors.

Question in MY QUESTIONS
Basic rules of derivatives

Question in Demos
Contains some extremely basic code to do symbolic differentiation: it can give the derivative of terms of the form $x^n$, $sin(x)$ and $cos(x)$, and apply the chain rule.

Question in Anna's workspace
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

Question in Shivendra's workspace
A graph is drawn. A student is to identify the derivative of this graph from four other graphs.
Version I. Graph is quadratic
Version II. Graph is horizontal
Version III. Graph is cubic
Version IV. Graph is sinusoidal

Question in Content created by Newcastle University
Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.
Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points  order of input and also giving that there is two stationary points.

Question in Content created by Newcastle University
Unit normal vector to a surface, given in Cartesian form.

Question in Content created by Newcastle University
Directional derivative of a scalar field.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$. Find $g(x)$.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Question in Content created by Newcastle University
Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

Question in Content created by Newcastle University
The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Question in Content created by Newcastle University
The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m1}(ax^2+b)^{n1}g(x)$. Find $g(x)$.

Question in Interactive graphs for MOOC
JSXGraph code based on original by Christian LawsonPerfect

Question in ME420 20192020 drafts
The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

Question in ME420 20192020 drafts
The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

Question in ME420 20192020 drafts
The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Question in Andreas's workspace
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*v1v2 
Question in 1202
A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Question in Calculus Math 5A
A basic introduction to differentiation

Question in Calculus Math 5A
Given the derivatives of a cubic function at a point, find the value of the function at another point.

Question in Calculus Math 5A
Given a set of curves on axes, generated from a function and its first two derivatives, identify which curve corresponds to which derivative.

Question in Calculus Math 5A
A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.