 First order differential questions and answers

Recent questions in First order differential equations nemired9 2021-12-26 Answered

What is the derivative of $$\displaystyle{h}{\left({x}\right)}={\sin{{2}}}{x}{\cos{{2}}}{x}$$ prelimaf1 2021-11-20 Answered

Find all first-order partial derivatives of the function at any point of the domain. $$\displaystyle{f{{\left({x},{y},{z}\right)}}}={4}{x}^{{{3}}}{y}^{{{2}}}-{e}^{{{z}}}{y}^{{{4}}}+{\frac{{{z}^{{{3}}}}}{{{x}^{{{2}}}}}}+{4}{y}-{x}^{{{16}}}+{2021}$$ tapetivk 2021-11-11 Answered

Look at the Chain Rule formula with a visual explanation of how it works: $$\displaystyle{\left({h}{\left({x}\right)}\right)}'={\left({g{{\left({f{{\left({x}\right)}}}\right)}}}\right)}'={g}'{\left({f{{\left({x}\right)}}}\right)}\cdot{f}'{\left({x}\right)}$$ $$\displaystyle{g{{\left({f{{\left({x}\right)}}}\right)}}}$$-outside function $$\displaystyle{\left({f{{\left({x}\right)}}}\right)}$$-inside function $$\displaystyle{g}'{\left({f{{\left({x}\right)}}}\right)}$$-derivative of the otside at f(x) $$\displaystyle{f}'{\left({x}\right)}$$-derivative of the inside Now, explain what happens in regards to calculating the derivative, if f(x) is also a composite function. remolatg 2021-09-25 Answered

If $$\displaystyle{f{{\left({x}\right)}}}+{x}^{{2}}{\left[{f{{\left({x}\right)}}}\right]}^{{5}}={34}$$ and f(1) = 2, find f '(1). sodni3 2021-09-06 Answered

Identify the surface whose equation is given. $$\displaystyle\rho={\sin{\theta}}{\sin{\phi}}$$ Tobias Ali 2021-07-05 Answered

Write first-order differential equations that express the situation: The increase in the number of people who have heard a rumor in a town of population 20,00020,000 is proportional to the product of the number PP who have heard the rumor and the number who have not heard the rumor at time tt . Lennie Carroll 2021-06-10 Answered

Write first-order differential equations that express the situation: A student in an engineering course finds the rate of increase of his grade point average GG is directly proportional to the number NN of study hours/week and inversely proportional to the amount AA of time spent on online games . Zoe Oneal 2021-05-31 Answered

Identify the surface whose equation is given. $$\rho= \sin \theta \sin \phi$$ nitraiddQ 2021-05-27 Answered

Write first-order differential equations that express the situation: A Walking Mode, l Construct a mathematical model to estimate how long it will take you to walk to the store for groceries. Suppose you have measured the distance as 11 mile and you estimate your walking speed as 33 miles per hour. If it takes you 2020 minutes to get to the store, what do you conclude about your model? Jason Farmer 2021-05-26 Answered

Write the following first-order differential equations in standard form. $$\displaystyle{y}'={x}^{{{3}}}{y}+{\sin{{x}}}$$ Khaleesi Herbert 2021-05-23 Answered

Find the differential of each function. (a) $$y = \tan \sqrt{t}$$ (b) $$y= \frac{1-v^2}{1+v^2}$$ Yasmin 2021-05-22 Answered

Write the following first-order differential equations in standard form. $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}={y}{x}{\left({x}+{1}\right)}$$ facas9 2021-05-05 Answered

If $$f(x) + x^2[f(x)]^5 = 34$$ and $$f(1) = 2,$$ find $$f '(1).$$ aflacatn 2021-05-03 Answered

How do you solve linear first-order differential equations? Lennie Carroll 2021-05-01 Answered

Solve differential equation $$xy'+2y= -x^3+x, \ y(1)=2$$ BolkowN 2021-03-09 Answered

Solve differential equation $$y '(t) = -3y + 9$$, $$y(0) = 4$$ BenoguigoliB 2021-03-09 Answered

Solve differential equation $$\frac{dy}{dx}+(\frac{a}{x})y=40x$$, for $$x>0$$ and $$y(1)=a$$ Dottie Parra 2021-03-08 Answered

Solve differential equation $$\displaystyle{y}'+{y}={x},\ {y}{\left({0}\right)}={1}$$ chillywilly12a 2021-03-08 Answered

Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{x}}}{{{y}}}},\ {y}{\left({0}\right)}=-{8}$$ tricotasu 2021-03-08 Answered

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