What is the 2x power differential of E

What is the 2x power differential of E

The differential is 2 (e ^ 2x)
The integral is 1 / 2 (e ^ 2x)

Find the differential of - 2x power sin (3 + 5x) with known y = e

Y '= e ^ (- 2x) * (- 2x)' sin (3 + 5x) + e ^ (- 2x) * cos (3 + 5x) * (3 + 5x) '= e ^ (- 2x) * - 2) sin (3 + 5x) + e ^ (- 2x) * cos (3 + 5x) * 5 = - 2E ^ (- 2x) sin (3 + 5x) + 5E ^ (- 2x) cos (3 + 5x) original differential dy = [- 2E ^ (- 2x) sin (3 + 5x) + 5E ^ (- 2x) cos (3 + 5x)]dx

Let the function y = x2 power 1, find the differential of the function 2, find the differential of the function at x = 3, find the differential of the function at x = 3 when the triangle x = 0.001, The error between differential and function increment is discussed,

1.y'=2x
2.y'(x=3)=2*3=6
3. Function increment △ Y / △ x = (x2 ^ 2-x1 ^ 2) / (x2-x1) = x2 + x1
When x = 3 △ x = 0.001, X1 = 3 x2 = 3.001
△y/△x=3.002
Error between differential and function increment = 6-3.002 = 2.998

1. The tangent slope of the x power of curve y = x + e at point (0,1) 2. Let the square of function y = x * y + the square of X - the cube of Y, then the total differential DZ =?

y=2x+1
The second question is vague

Higher number differential problem, x = 1 + T ^ 2, y = cos, t d ^ 2Y / D ^ 2x = ()

dy/dx=dy/dt/dx/dt=-sint/2t,d^2y/dx^2=(dy/dx)/dt/dx/dt=(-2tcost+2sint)/8t^3

Differential y = ln (1-x ^ 2) y = e ^ - x + cos (3 + x) y = sin2x

-((2x)/(1-x^2))dx;
(-E^-x-Sin[3+x])dx;
2Cos[2x]dx