derivatives

1. On process, and on the derivatives of the powers of sine

Some background: A few months ago, I was on holiday in Prague. And I saw a nice clock there. Which led me to think about the equation of time. Which led me to think about y = x + e\,\sin y Which led me to think about \frac{e^k}{k!} \frac{\partial^{k-1}}{\partial x^{k-1}} [\sin^k x] Which...
2. derivatives

A hammer was dropped from the pocket of a constructor from a height of 288 ft building and falls toward the earth in a straight line. In t seconds the hammer drops a distance of s=32t^2 ft. a) How many seconds after drop does the hammer hit the ground?:confused: b)What is the average velocity...
3. Limes superior and inferior inequalities with functions and its derivatives

Hi, I have got some troubles with Lemma 2. from N.H. Duu, On The Existence of Bounded Solutions for Lotka- Volterra Equations, Acta Mathematica Vietnamica 25(2) (2000), 145-159. Can anybody help me understand the last part of this proof? Exactly, how this transformation using Cauchy theorem...
4. Which of the following statements is correct ?

This is a question from a college admission exam. There is a mistake in the attachment. f is derivative not differentiable.
5. Derivatives

Differentiate the function below y = (3x^2 + 2x + 1)/(4x^2 - 5x) This question is giving me much headaches as my assignment due date is tomorrow morning. May somebody help please
6. Derivatives

Differentiate the function below with respect to x. y = In (âˆš4x^3 + 3x^2 + 2x). May somebody help please.( The whole expression is in square root).
7. How do I deal with a Fourier transform that contains derivatives?

I want to calculate this: \frac{1}{2 \pi } \int_{- \infty}^{\infty} |X(Ï‰)|^2 dÏ‰ Should I just normally calculate the derivative inside of X(Ï‰) and then use that final form of Î§(Ï‰) to calculate the integral? Or can I use somehow the property which says that the Fourier transformation...
8. "Finding Inflection Points" Math Problems Help #2

"Finding Inflection Points" Math Problems Help 4 Let f(x)=-2x^6+15x^5. For what values of x does the graph of f have a point of inflection? I found the second derivative and when factored leaves me with: -60x^3(x-5). So, I figured the answer is just x=5 but my friend told me its zero as...
9. "Finding Inflection Points" Math Problems Help 3

Ok this other inflection problem: Let h(x)=x^5+5x^4. For what values of x does the graph of h have a point of inflection? I am stuck on what to do after the second derivative which I found was: 6x^1+60x^2. I tried to factor it which gave me: 6(10x^2+x), but then I don't now how else to factor...
10. "Finding Inflection Points" Math Problems Help

I am just learning this new topic at school, and was hoping that you can help me with this example my teacher provided me. The problem is: Let f(x)=-2x^4-8x^3+180x^2. For what values of x does the graph of f have a point of inflection? I understand that you have to do something with the second...
11. Derivatives of a function

Hello, Calculate the derivatives of the function: 1) f(x)=x! 2) f(x)=(2-\sqrt{2})\cdot (2-\sqrt[3]{2})\cdot \dots \cdot (2-\sqrt[x] {2}). All the best, Integrator
12. Derivatives

The answer in my book is 5 but if we put 5 instead of x all of them are differentiable
13. Rate change and derivatives

An arrow is shot upward on a planet. Its height (in meters) after t seconds is given by h(t) = 60t â€“ 0.6t^2. a. At what time will the arrow reach the top? b. With what velocity will the arrow hit the ground?
14. Solving a 3 variables equation, one happens to cause an oddity

Hey, so we had this question in class: Given that the relationship between distance (m) and velocity (v) of an object is v^2 = 1 - m^3 Find the acceleration of the object when m=1 By taking the derivative of each side with respect to t 2v \frac{dv}{dt} =...
15. Derivatives Video!!

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Hey. So we had this question: Given that f(x) = f(x+h) - 5x^3 h, find f'(x)? So our teacher solved it in two ways, one of them was this: f(x+h) - f(x) = 5x^3 h \large\lim\limits_{h \to 0} \large\frac{f(x+h) - f(x)}{h} = \large\lim\limits_{h \to 0} \large\frac{5x^3 h}{h} f'(x) =...
17. Derivatives help

Good morning, I was wondering if someone can give me a clear explanation of how to solve for derivatives? Please somebody help me... also what does it mean to solve for "the first derivative"? f(x)=â…“ x2 +7x - 4 f(x)= 5 x3+3x Thank you!
18. Challenging Derivatives of Exponential and Sinusoidal Functions task question

A common brand contains 30 mg of codeine. Since it is physically addictive and has other unwanted side effects, it is important to avoid an overdose while helping to relieve pain symptoms such as those caused by a headache. Samples of blood were taken at regular time intervals from a patient who...
19. Partial derivatives

Please could someone assist me with this question please I'm so lost. w=x^8+10xyz+y^9z^8 x=r^5-s^8 y=10rs z=5r-5s Find dw/ds and dw/dr
20. QUick converging mimimization without derivatives?

We have three points: x_0, x+h and x-h. We interpolate parabola using Stirling formula. Next, x:=parabola extreme. We can much decrease h and have next 3 points:x_0, x+h and x-h. One problem: fast decreasing accuracy because of zero in denominator. static double f(double x)...