Tagged Questions
3
votes
2answers
66 views
Why is this derivative incorrect?
We have to find the derivative of $$f(x) = \dfrac{\tan(2x)}{\sin(x)}$$
I would like to know why my approach is incorrect:
$$f'(x) = \dfrac{\sin(x) \cdot \dfrac{2}{\cos^2(2x)} - \tan(2x) \cdot ...
1
vote
2answers
37 views
Derivative of Trig Functions (Intuition Help?)
Looking for some intuition help here.
I have the following exercise and these are the steps I take:
$$
y = \sin\left(\frac{1}{x}\right)
$$
$$
u=\frac{1}{x}
$$
$$
y = \sin u,\;\;\frac{dy}{du} = \cos ...
-2
votes
2answers
35 views
Calculus help needed.
In this question you must demonstrate knowledge of derivatives and the use of the differentiation rules, as well as basic algebra. Hence, you must show your working.
Any help is much appreciated!
2
votes
5answers
371 views
The hypotenuse of a right angle triangle measures 12 cm. What size angles would produce maximum…
The hypotenuse of a right angle triangle measures 12 cm. What size angles would produce the maximum perimeter?
I got to point where I take the derivative and get $12(\cos\theta-\sin\theta)=0$, not ...
0
votes
3answers
62 views
Differentiate $y = {(x + 2)^3}{(1 - \sin 2x)^2}{(1 + \tan x)^3}$
I haven't got very far in attempting this:
$\eqalign{
& y = {(x + 2)^3}{(1 - \sin 2x)^2}{(1 + \tan x)^3} \cr
& y = {\left( {(x + 2)(1 + \tan x)} \right)^3}{(1 - \sin 2x)^2} \cr} $
I'm ...
1
vote
1answer
62 views
Differentiation of a natural log with fraction of trigonometric functions
I am starting with differenciation and I stumbled upon the following exercise:
Find $\frac{df(x)}{dx}$, where
$$f(x)=\ln \left({\cos x + \sin x \over \cos x - \sin x}\right).$$
So I applied the chain ...
2
votes
2answers
168 views
Finding the 9th derivative of $\frac{\cos(5 x^2)-1}{x^3}$
How do you find the 9th derivative of $(\cos(5 x^2)-1)/x^3$ and evaluate at $x=0$ without differentiating it straightforwardly with the quotient rule? The teacher's hint is to use Maclaurin Series, ...
2
votes
2answers
43 views
Help with $\arcsin(x)$ derivative and differentials.
I'm watching this video lecture
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-11-chain-rule/ and I'm stuck at around 3:40, I can't seem to ...
1
vote
1answer
78 views
Finding $f'''(x)$ of $f(x)=\sin{\pi}x$
Finding $f'''(x)$ of $f(x)=\sin{\pi}x$.
First
$$f'(x)=\frac{d\sin{\pi}x}{d({\pi}x)}\frac{d({\pi}x)}{dx} ={\pi}\cos{\pi}x$$
Second
$$f''(x)=-{\pi^2}\sin{\pi}x$$
Third
$$f'''(x)= -{\pi^3}\cos ...
1
vote
1answer
31 views
Maximum value of the given expression
Assuming $\theta \in [\frac{-5\pi}{12},\frac{-\pi}{3}]$, find the maximum value of
$$\frac{\tan(\theta+\frac{2\pi}{3})-\tan(\theta+\frac{\pi}{6})+\cos(\theta+\frac{\pi}{6})}{\sqrt{3}}$$
I know we can ...
2
votes
2answers
83 views
Derivative of $\cos nx$
How to calculate derivative of $ \cos nx$? Do I need any formula for $ \cos nx$?
The answer in my exercise book says it is $-a \sin ax$. But I don't know how to come to this result. Could you maybe ...
0
votes
1answer
123 views
Problem with finding critical point of trig function
Can anyone help me out solving this? I don't understand how my professor ends up with
$$
1 - \frac{1}{2\sin^2(x/2)}
$$
Thanks everyone!
The problem is stated in this picture: http://imgur.com/z8yw2
0
votes
2answers
42 views
Find the coefficients of a polynomial given a tangent
Can someone help me with this problem please? (Thanks in advance):
The graph of $y=3x$ is tangent to $f(x)=2x^2-ax+b$ at $x=2$. Find the values of $a$ and $b$.
0
votes
2answers
82 views
How to differentiate e to a function?
I am trying to find the derivative of $$\large e^{2 \pi i t \sin(\pi/(2t))}.$$
I know that I am to take the derivative of the exponent, and then multiply it by the beginning problem - the piece that ...
1
vote
0answers
71 views
Bounding derivative of a function
Consider $a(t)\in\mathbf{L}^{2}(\mathbb{R})$ and $a(t)>0$, is a low pass smooth function with $\hat{a}(f)=0, |f|>f_{max}$. Can we have a upper bound on the following,
...
1
vote
5answers
194 views
Derivate of $(\sin \theta)^{n-1}$
Please, explain me why the derivative of $$(\sin \theta)^{n-1} = (n-1)\cos\theta \cdot (\sin \theta)^{n-2}$$
Thanks so much!
0
votes
2answers
103 views
Derivatives of trig functions
How can I prove that $\frac{d}{dx} (\csc x)= -\csc x \cot x$?
Specifically, how does one see the step $\cos x/\sin x = \cot x$?
2
votes
6answers
185 views
Why isn't $\frac{d}{dx} \sin (2x) = \cos (2x)$?
$g=\sin$, $g'=\cos$
If $g(x)=\sin(x)$, then $g'(x)=\cos(x)$.
Then $g(y)=\sin(y)$ and $g'(y)=\cos(y)$.
Let $y=2x$.
Then $g(y)=\sin(2x)$ and $g'(y)=\cos(2x)$, but if $h(x)=\sin(2x)$, then ...
2
votes
4answers
135 views
Find $\frac{d}{dx}(\cos x)$
Find $\dfrac{d}{dx}(\cos x)$
I know the answer is $-\sin x$ only by process of elimination. I can find solution graphically but I need to know algebraically. Here is my proof so far.
...
0
votes
2answers
96 views
Stuck With The Differentiation Of A Inverse Hyperbolic Function
I'am suppose to show that $$\frac{\mathrm{d} }{\mathrm{d} x}[x \operatorname{cosh}^{-1}(\cosh x)] = 2x$$
And this is what i've tried.Upon differentiating the above function wrt $x$ using the product ...
6
votes
4answers
237 views
Nth derivative of $\tan^m x$
$m$ is positive integer,
$n$ is non-negative integer.
$$f_n(x)=\frac {d^n}{dx^n} (\tan ^m(x))$$
$P_n(x)=f_n(\arctan(x))$
I would like to find the polynomials that are defined as above
...
8
votes
5answers
639 views
Calculating the shortest possible distance between points
Question:
Given the points $A(3,3)$, $B(0,1)$ and $C(x,0)$ where $0 < x < 3$, $AC$ is the distance between $A$ and $C$ and $BC$ is the distance between $B$ and $C$. What is x for the distance ...
2
votes
1answer
67 views
Need help understanding $\frac {dx}{\cos^2(\frac{x}{2})} = 2d(\operatorname{tg}(\frac{x}{2})) $
I have found this statement somewhere, however, I dont really understand it.
Could someone explain me where does $2$ before $\operatorname{tg}(x/2)$ come from?
$$\frac {dx}{\cos^2(\frac{x}{2})} = ...
12
votes
2answers
441 views
Zeroes of the third derivative of an iterated sine.
I've been playing with the functions $$f_n:[0,\pi/2]\to[0,1]\\\begin{cases} f_1&=&\sin\\f_{n+1}&=&\sin\circ f_n\end{cases}.$$ A simple argument proves that $f_n(x)\to 0$ for $x\in ...
2
votes
1answer
179 views
Differentiate an Inverse Function, Two Methods?
I would like to take the derivative of this inverse function at $\pi$: $f(x) = 2x + \cos{x}$, given that ${f}^{-1}(\pi) = \frac{\pi}{2}$.
I know that there are two methods of doing it. Let me ...
2
votes
2answers
122 views
Changing the argument for a higher order derivative
I start with the following:
$$\frac{d^n}{dx^n} \left[(1-x^2)^{n+\alpha-1/2}\right]$$
Which is part of the Rodrigues definition of a Gegenbauer polynomial. Gegenbauer polynomials are also useful in ...
0
votes
1answer
143 views
AP Calculus Homework Help Needed
I am having another problem with basic math in my homework. Help is much appreciated.
The answer is: $\frac 1{\sqrt{4-x^2}}$
The problem is: Find $\frac {\mathrm{d}}{\mathrm dx} \sin^{-1} (x/2)$
...
