- #1
yonathan
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can u pls help me with this quaestion?
p=Po e^-h/c
p=Po e^-h/c
Welcome to PF yonathan,yonathan said:can u pls help me with this quaestion?
p=Po e^-h/c
Notice that the two derivatives that you have found are not equivalent:yonathan said:the pressure P of the atmosphere at height 'h' above ground level is given by P=Po e^-h/c where Po is the pressure at ground level and c is the constant.determine the rate of change of pressure with height when Po=1.013*10^5 pascals C=6.05*10^4 at 1450 meters.
i used the for differentiation to differentiate it and find the first derivative of P=Po e^-h/c and i got P=C*Po e^-h or P=Po*(-h/c) e^-h/c and i substitute ted the numbers the given and my calculator seems not to find the ans for it. so can u help me find the derivitive of P=Po e^-h/c? pls?
So, which one is it?yonathan said:P=C*Po e^-h or P=Po*(-h/c) e^-h/c
Are you sure about that?yonathan said:the derivative of e^f(x) is (f)e^f(x)
Simply let:yonathan said:but what if it was e^(F/x) that's what i want to find out??
No it isn't, you need to recheck you derivative. Use the chain rule.yonathan said:so the first derivative of Po e^-h/c is dp/dh=Poe^f(h), where f(h)is -h/c, and after this, all i have to do is substitute the numbers given, yeh? and i am sure about the derivative u asked me.
Note that in this case, h is a variable and not constant. The chain rule states that for a composite function [itex]y\left(f(x)\right)[/itex]yonathan said:what is 'f' in ur chain rule cause according to it the derivative is f(h)is -h/c??
Okay, let's take this a term at a time. What is:yonathan said:sorry i still don't follow, can u explain it to me in another way or something? i don't know wat to do with the last answer u gave me. do i substitute my numbers on ur answer and wat is e^f(h), how am i suppose to solve it?
It represents the derivative of P with respect to h, which is not P.yonathan said:it represents the differentiation of P which is P.
A differential equation is a mathematical equation that describes how a quantity changes over time or in relation to other variables. It involves derivatives, which represent the rate of change of the quantity being studied.
The purpose of solving a differential equation is to find a function that satisfies the equation and represents the behavior of the quantity being studied. This allows us to predict future values and understand the underlying processes that govern the system.
The main types of differential equations are ordinary differential equations, which involve a single independent variable, and partial differential equations, which involve multiple independent variables. Additional classifications include linear vs. nonlinear, and first-order vs. higher-order differential equations.
There are many methods for solving differential equations, including separation of variables, substitution, Euler's method, and numerical methods such as Runge-Kutta and finite difference methods. The appropriate method depends on the type and complexity of the equation.
Differential equations are used in a variety of fields, including physics, engineering, economics, and biology, to model and understand natural phenomena. They are particularly useful for predicting how systems will change over time, such as in population dynamics, chemical reactions, and electrical circuits.