Proving dy/dx = (a+4b)x^(a+4b-1) for y = x^(2a+3b)/x^(a-b), a and b Integers

  • Thread starter Thread starter tofu
  • Start date Start date
  • Tags Tags
    Calculas
AI Thread Summary
To prove that dy/dx = (a+4b)x^(a+4b-1) for y = x^(2a+3b)/x^(a-b), the expression can be simplified to y = x^(a+4b). The derivative of y, denoted as y', is calculated using the power rule. Applying the power rule yields y' = (a+4b)x^(a+4b-1). Thus, the proof confirms that dy/dx indeed equals (a+4b)x^(a+4b-1).
tofu
Messages
4
Reaction score
0
Show that dy/dx = (a+4b)x^(a+4b-1) if y = x^(2a+3b) / x^(a-b) and a and b are integers



thx
 
Physics news on Phys.org
If you have
<br /> y=\frac{fx}{gx}<br />
then
<br /> \frac{dy}{dx}=\frac{gx*(fx)&#039;-fx*(gx)&#039;}{(gx)^2}<br />
 
Much more simply:
y = x^(2a+3b) / x^(a-b)
= x^((2a+3b)-(a-b))
= x^(a+ 4b)

Now, what is y'?
 

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 »

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 »

Similar threads

MHB Solve Polynomial Division: -5a + 4b = x^2+1 Rem -A-2
Replies
1
Views
1K
##\int_0^1 F_x(x,0)dx + \int_0^1 F_y(1,y)dy##
Replies
7
Views
1K
Find an integer having the remainders ## 1, 2, 5, 5 ##
Replies
7
Views
2K
MHB -2.2.35 Show that dy/dx=(x+3y)/(x-y) is homogeneous. and....
Replies
2
Views
1K
Determine the x- and y-coordinates of the trapezoidal shape.
Replies
2
Views
3K
B Expressions of ##log(a+b), tan^{-1}(a+b),sin^{-1}(a+b)##,etc
Replies
12
Views
2K
MHB Point (a, b) Reflected About Two Lines
Replies
3
Views
2K
MHB Inequality: $(1+a)^7(1+b)^7(1+c)^7 > 7^7 a^4b^4c^4$
Replies
5
Views
2K
Normalization constant for a 3-D wave function
Replies
2
Views
4K
Characteristic equation with x^2 coefficient
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top