how do you prove that the derivative of x^n is nx^n-1

how do you prove that the derivative of x^n is nx^n-1

Calculus Question - Please help An object is thrown from a height H above an uneven ground described by a height function h(x). Suppose that the object can be thrown with maximum velocity v at...

I', really stuck on this one HW question: I have to show how dC/dt = (D * (d^2C/dx^2)) + P at steady state (so when cD/dt =0) equals: (d^2C/dz^2) + (Pa^2/D...

I know to like assume that (x^5)+(e^x)=0 has two distinct roots and then find the contradiction. But am stuck.

I need help answering this word problem...I need to find the function P(t) and I just can't remember the process whatsoever "A company has its profit function P(t) defined since...

(f1+f2+f3+...)'=f1'+f2'+f3'+...

Use linear approximation and differential to approximate: sin 31`

derivative

if y=sinx+tanx+10 find dy/dx and show that when x=pi radian , y+dy/dx=10

Find the derivative of the following functions: d^2 / dx2 (x sin x)

I couldn't understand and sole this question. please help Define f(x):= (x-a1)(x-a2)(x-a3)... (x-at), where an are constants, 1≤n≤t , where t is some finite natural number. Show...

The acceleration due to gravity, g; is given by g = GM / r2 ; where M is the mass of the earth, r is the distance from the center of the earth, and G is the universal gravitational...

Use linear approximation and differential toto approximate : 14^(1/4)

The de?finitions of derivative of two functions f and g are given by: f' (x) = lim f(x + Δx) - f (x) / Δx , g'(x) = lim g(x + Δx) - g(x) / Δx ...

(a) Find the average velocity of the particle over the interval [1; 3] seconds. (b) Find the instantaneous velocity of the particle at t = 1 second.

find the derivative of f(x) = √x+1 at x = 0 the derivative is 1/2x2, but i want to know the long way f(x+h)/h-f(x)/h method, thanks in advance

Let g(x) = |cos x|. (a) Graph g(x) and g'(x) on one graph for −2π ≤ x ≤ 2π (b) find g'(π/2) how would you show that it doesn't exist. (c) g'(...

Show that there is no polynomial function that has a derivative of x^-1.

I need help proving this derivative using the difference quotient. prove derivative of x^n