How to Correctly Apply the Quotient Rule in Differentiation?

DollarBill
Messages
44
Reaction score
0

Homework Statement


X / 1+sinX

The Attempt at a Solution


Quotient rule

(1+sinX)(1)-X(1+cosX) / (1+sinX)2

To:

1+sinX-X-XcosX / (1+sinX)2

But when I look at the answer in the back of the book, it's wrong.
 
Physics news on Phys.org


Is the derivative of 1+sinX really 1+CosX? I thought the derivative of 1 was zero. ;0)
 


I always make these stupid mistakes

Thanks :biggrin:
 

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

How Does Substitution Affect Double Integration and Differentiation?
Replies
3
Views
1K
Derivative of a sinusoidal function
Replies
2
Views
1K
Method of Undetermined Coefficients
Replies
1
Views
2K
How to Solve a Second Order Nonhomogeneous Differential Equation?
Replies
9
Views
2K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
Replies
3
Views
2K
Rules to apply L'Hospital on a limit
Replies
12
Views
2K
Find the limit using taylor series
Replies
11
Views
3K
Differentiation of Log(cos(X)/x^2)^2
Replies
6
Views
2K
##\int (\sin x + 2\cos x)^3\,dx##
Replies
5
Views
2K
Calculation of limit. L'Hopital's rule
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top