Calculators AI Whiteboard Worksheets & Tests
Book solutions
Algebra Baldor
Go Premium Topics

Find the derivative $\frac{d}{dx}\left(\ln\left(x\right)\tan\left(\frac{x}{2}\right)-\cot\left(x\right)\ln\left(x\right)\right)$ using the sum rule

Used Formulas

Go!
Symbolic mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch
Solving: $\frac{d}{dx}\left(\ln\left(x\right)\tan\left(\frac{x}{2}\right)-\cot\left(x\right)\ln\left(x\right)\right)$
Solve instead: $\frac{d}{dx}\left(ln\tan\left(\frac{x}{2}\right)-\cot\left(x\right)\ln\left(1+\sin\left(x\right)-x\right)\right)$

Solution

Formulas

Videos

Basic Derivatives

· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Product rule for derivatives
$\frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$
$\frac{d}{dx}\left(\frac{x}{c}\right)=\frac{1}{c}\frac{d}{dx}\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
· Derivative of the natural logarithm
$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$

Derivatives of trigonometric functions

· Derivative of tangent function
$\frac{d}{dx}\left(\tan\left(\theta \right)\right)=\frac{d}{dx}\left(\theta \right)\sec\left(\theta \right)^2$
· Derivative of cotangent function
$\frac{d}{dx}\left(\cot\left(\theta \right)\right)=-\frac{d}{dx}\left(\theta \right)\csc\left(\theta \right)^2$
· Derivative of the sine function
$\frac{d}{dx}\left(\sin\left(\theta \right)\right)=\cos\left(\theta \right)$

Function Plot

Plotting: $\frac{\tan\left(\frac{x}{2}\right)}{x}+\frac{1}{2}\ln\left(x\right)\sec\left(\frac{x}{2}\right)^2+\csc\left(x\right)^2\ln\left(x\right)+\frac{-1}{1+\sin\left(x\right)-x}\cot\left(x\right)\left(\cos\left(x\right)-1\right)$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

$\frac{d}{dx}\left(\sqrt{\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}}\right)$

$\frac{d}{dx}\left(\ln\left(\mathrm{sech}\left(3x+8\right)\right)\right)$

$\frac{d}{dx}\ln\left(x^2+1\right)$

$\frac{d}{dx}\left(\ln\left(1+x\right)\right)$

$\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$

$\frac{d}{dx}\left(x\sqrt{x^2+1}\right)$

Find the derivative

$\frac{d}{dx}\left(x^2+y^2\right)$

Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

See formulas (10)

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account