Find derivatives of the functions defined as follows.y=(te^t=2)/(e^(2t)+1)

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders? Give examples.

Use the given graph to estimate the value of each derivative.(Round all answers to one decimal place.)Graph uploaded below.
(a) f ' (0)1
(b) f ' (1)2
(c) f ' (2)3
(d) f ' (3)4
(e) f ' (4)5
(f) f ' (5)6

With $f(x)=e^{4x+1}$ and $g(x)=7x^2+5$, find the derivative of the compostion f(g(x)).

Derivatives of products and quotients Find the derivative of the following functions by first expanding or simplifying the expression.
${\displaystyle f\left(w\right)=\frac{w^3-w}{w}}$

Find the derivative of (f*g)(x), where $f(x)=2x^2+3$ and $g(x)=7x^3+3x+5$.

Find the second partial derivatives for the function ${\displaystyle f(x,y)=x^4-3x^2{y}^2+y^2}$ and evaluate it at the point(1,0).

Find the derivative of the following function.
${\displaystyle y=x^5}$