Learn the Chain Rule for Finding the Derivative of e^sec(x) | Homework Question

  • Thread starter Thread starter alpha01
  • Start date Start date
  • Tags Tags
    Chain Chain rule
alpha01
Messages
77
Reaction score
0

Homework Statement

derivative of esec(x)

The Attempt at a Solution

u = sec(x)
y = eu

du/dx = tan(x)sec(x)
dy/du = eu

dy/dx = dy/du * du/dx
= esec(x)tan(x)sec(x)
 
Physics news on Phys.org
alpha01 said:

Homework Statement




derivative of esec(x)



The Attempt at a Solution




u = sec(x)
y = eu

du/dx = tan(x)sec(x)
dy/du = eu

dy/dx = dy/du * du/dx
= esec(x)tan(x)sec(x)
Looks good to me :approve:
 
thanks
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

The below solution seems to assume that 1/0 = 0
Replies
7
Views
1K
Solve the given differential equation
Replies
10
Views
2K
Chain Rule with Leibniz Notation
Replies
4
Views
2K
Find the length of the curve C
Replies
1
Views
1K
Solve this problem that involves implicit differentiation
Replies
15
Views
2K
Calculating 2nd Total Derivative of u w.r.t. t
Replies
28
Views
3K
Implicit differentiation: why apply the Chain Rule?
Replies
3
Views
1K
Can you handle this integration with limits problem?
Replies
3
Views
2K
Finding the Derivative of y=sqrt(x+sqrt(x+sqrt(x)))
Replies
7
Views
3K
Understanding the Derivative of y with Respect to x
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top