👉 Try now NerdPal! Our new math app on iOS and Android

# Find the derivative $\frac{d}{dx}\left(\frac{\tan\left(x\right)}{1+x}\right)$

## Step-by-step Solution

Go!
Math 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
Dx
|◻|
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

###  Videos

$\frac{\left(1+x\right)\sec\left(x\right)^2-\tan\left(x\right)}{\left(1+x\right)^2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by $h(x) = \frac{f(x)}{g(x)}$, where ${g(x) \neq 0}$, then $h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}$

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

Learn how to solve integral calculus problems step by step online.

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

Learn how to solve integral calculus problems step by step online. Find the derivative d/dx((tan(x)/(1+x)). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

$\frac{\left(1+x\right)\sec\left(x\right)^2-\tan\left(x\right)}{\left(1+x\right)^2}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of tanx/(1+x) using the product ruleFind derivative of tanx/(1+x) using the quotient ruleFind derivative of tanx/(1+x) using logarithmic differentiationFind derivative of tanx/(1+x) using the definition

SnapXam A2

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
Dx
|◻|
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

### Main topic:

Integral Calculus

###  Join 500k+ students in problem solving.

##### Without automatic renewal.
Create an Account