Solving Derivatives: Tips & Tricks

  • Thread starter Thread starter Styx
  • Start date Start date
  • Tags Tags
    Derivative
Styx
Messages
27
Reaction score
0
I'm not sure if I have been doing this one right, or where I can go from here...
 

Attachments

  • Equation.jpg
    Equation.jpg
    15.9 KB · Views: 613
Physics news on Phys.org
Your first line was correct, but leave the working at the 2nd line.
 
Your second line is incorrect-- you forgot to apply the chain rule.
 
Oops that reminds me, Rewrite my last post as 1st and 2nd lines of working.

The 1st line of working you forgot the chain rule, however you rectified the error on the next line.
 
Use the chain rule, u=3x^2+5,u'=6x,v=2x^2-x,v'=4x-1,y=vu^8,y'=8vu^7 so dydvdu/dvdudx=dy/dx
 

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

Find nth derivative of e^m(arcsinx) where x=0
Replies
7
Views
2K
Multivariable calculus problem involving partial derivatives along a surface
Replies
9
Views
2K
Understanding Iterative Derivatives of Log Functions
Replies
12
Views
2K
Find Values of Osculating Circle Tangent to a Parabola
Replies
4
Views
1K
Derivation or proof of derivative sin (x)
Replies
25
Views
2K
Finding formula for nth derivatives of some functions
Replies
3
Views
1K
Exam asks me for a case where ▲x > dx?
Replies
5
Views
1K
How do I compute the derivative of (x^x)^(x^x)^(x^x)....
Replies
29
Views
2K
Existence of directional derivative
Replies
4
Views
1K
Why Does the Multidimensional Chain Rule Lead to Euler's Theorem Proof?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top