# derivatives

1. ### Help with a Derivative question that involves Sin

Hey i have this question given to me by teacher that i just cant wrap my head around i know the derivative of sin(x) is cos(x) but the way its done confuses me here's the question: The self induced e.m.f (measured in volts, V) in an inductor can be found by using: e= L V, where L is the...
2. ### Optimization problem - rectangle inscribed in a triangle

Hi, I'm trying to solve for the following problem: "determine the area of the largest triangle that can be inscribed in a right triangle with legs adjacent to the right angle that are 5 cm and 12 cm". This is how I solved the problem: I got the correct solution. However, now I'm curious...
3. ### Power of a function rule v.s. chain rule

Hi, I'm hoping that someone can provide some insight on the following definition: I'm wanting to understand how this rule is really any different from the chain rule. According to my textbook, the power of a function rule is a special case of the chain rule, but I don't particularly...
4. ### Trying to find partial derivatives

I have an implicit equation relating P1, P2, Q: P1 - P2 - k * ( f(P1,Q) + g(P2,Q) ) = 0 ie. given P1, P2, I can find Q by iteration. I know the functions f and g and also have their analytical derivatives. I need to find partial derivatives dQ/dP1 and dQ/dP2
5. ### Implicit Differentiation

I have a function 4x^2-xy+3y^2=0 which I am asked to find the second derivative in terms of x. When I differentiate this implicitly I get y' = (-8x+y) / (x+6y) My question arises when I am differentiating this again but with the function broken up into two composite functions f(x) = (-8x+y) and...
6. ### Derivative: Delta of a Down and Out Call Option with Barrier=Debt(K)

0down votefavoriteFor I am trying to compute the derivative of this function with respect to V0: E0=V0*N(d1)-K*e^-rt * N(d2)-V0*(K/V0)^2l * N(d1b)+K*e^-rt *(K/V0)^(2l-2)*N(d2b) where d1=ln(V0/K)+(r+sigmaV^2/2) * t)/sigmaV*sqrt(t) d2=d1-sigmaV*sqrt(t) d1b=ln(K/V0)+(r+sigmaV^2/2) *...
7. ### Finding Equation of a Tangent Line without using Derivatives.

Hey, I'm new. I'm having some trouble. I'm given the problem: y = 4x-3x^2 , (2,-4) I'm unsure about what to do exactly. When do I use the slope of a line formula? When am I supposed to use point slope? When do I utilize the alternative ? Please, and thanks for the help!
8. ### finding derivatives when calculating taylor polynomial

Hi to calculate the taylor polynomial at T3(x) at 1 for f(x) =\frac{1}{x+2} I am having trouble finding the 3rd derivative. Dealing with a rational function so we use the quotient rule, 1st derivative =\frac{0.(x+2)-1(1)}{(x+2)^2}= \frac{-1}{(x+2)^2)} 2nd derivative (this is where I have seem...
9. ### Modeling and Optimization

The figure shows the graph of f(x)=xe^x, x greater than or equal to 0. figure: f(x) curve is drawn and under the max. point/ concave down curve there is an inscribed rectangle. with width from a(left) to b(right) and height up to a certain point of f(x). Let a > 0 and b > 0 be given as...
10. ### Simple question for complex derivatives

For "If f(z) and g(z) are differentiable, so is f(z)+g(z)", they have to be differentiable at identical z right? Like say f(z)=z (differentiable for all z), and g(z)=|z|^2 (differentiable of all z except 0), the sum rule wouldn't work right?
11. ### Partial Derivatives

I have this problem on the review for the final. When i worked it out, I got the bottom equation to be equal to 0. The bounds are x+2y and x-2y if you cant see it
12. ### How do I solve this?

For the functions: f(x)= 5x^3 and g(x)=4x^2, prove that the derivative of the sum of the functions is equal to the sum of the derivative of each function: [f(x)+g(x)]'= f'(x) + g'(x) (Worried) Need some help solving this question, tried different approaches from what I've learned but can't...
13. ### Is this correct? Rules of derivatives question

Not sure how to do this question because there is a coefficient in the front. Also should I factor in the 2 at the end? (Worried)
14. ### derivative of multiple integral

I have a problem in derivative of multiple integrals. for example i don't know how can I do it for the below question. would you please help me to solve it? thanks A= \int \int q(y,z)(Ln|z|+tr(z^{-1}(x'x-2 x' y+y' y)))dy dz where x,y,z are vectors we want derivative of A wrt q(y,z). please look...
15. ### Dont really understand partial derivatives

I'm not really sure what a partial derivative is...all I know is that the partial derivative is the slope of a multi variable function's intersection with a plane (meaning you are holding all other variables constant... as long as your plane is completely parallel to one of the x,y,,z...
16. ### Jacobian Determinant

I am having a hard time understanding this problem Imgur: The most awesome images on the Internet and I have no clue on where to start or go about it. I'm thinking of expanding gn and g{n+1} into its determinants , but I'm not sure so sure of how I get to the conclusion that they want me to...
17. ### Advanced Calculus Help on Jacobians

This problem from class on proving a certain matrix inductively and then seeing if its Jacobian Determinant matches the given formula has really confused me on how I should set it up and even solve it . If the image isn't visible, it's also in this imgur link: Imgur: The most awesome images on...
18. ### whole derivative in terms of partial derivatives

- using this equation - ??
19. ### Graphing with derivatives problem

Hello! I'm having a little trouble with this problem. f(x) = 11 - 6e-x I know the derivative is 6e-x, which means there are no critical points. And i know there is a horizontal asymptote at y=11. I need help finding where f(x) is increasing (using interval notation using the union U symbol)...
20. ### Different Derivatives or Not...Part A

What is the difference between d/dx [|sin x|] and d/dx [ln|sin x|]?