Why Does Differentiating y=sin(pix) Result in y'=cos(pix)*pi?

Thread starter h_k331
Start date Jun 19, 2005
Tags

Differentiation Trigonometric

AI Thread Summary

The differentiation of y=sin(pi*x) results in y'=cos(pi*x)*pi due to the application of the chain rule. When differentiating a function where the argument is a function of x, both the derivative of the outer function and the derivative of the inner function must be considered. In this case, the outer function is sin(u) and the inner function is u=pi*x. Therefore, the derivative of sin(u) is cos(u), and the derivative of u with respect to x is pi. Understanding the chain rule is essential for correctly differentiating composite functions.

Jun 19, 2005

h_k331

When y=sin(pi*x), why does y'=cos(pi*x)*pi, not y'=cos(pi*x)?

hk

Physics news on Phys.org

Jun 19, 2005

Integral

Staff Emeritus

Science Advisor

Homework Helper

Gold Member

It's the chain rule. when the argument of a trig function is a FUNCTION of x, you have take the derivative of the agrgument. So, in general

(f(g(x)))'= f'(g(x))*g'(x)

Jun 20, 2005

h_k331

So than in this case y=f(u)=sinu and u=g(x)=pi*x, correct?

Jun 20, 2005

OlderDan

Science Advisor

Homework Helper

h_k331 said:

So than in this case y=f(u)=sinu and u=g(x)=pi*x, correct?

That is correct.

Jun 20, 2005

h_k331

Thanks guys, I appreciate it.

hk

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .

View full post »

Thread 'I've come across another fluid pressure problem I don't understand'

Neglect gravity other than that of water; neglect friction. F1=ρgsh=1000*10*1*(1+4)=50000 N; F1=ρgsh=1000*10*0.1*4=4000 N; F3=50000-4000=46000 N?

View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

View full post »