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

## Step-by-step Solution

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sinh
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###  Videos

$\sec\left(x+1\right)^2$
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##  Step-by-step Solution 

Problem to solve:

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

Specify the solving method

1

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 ${f'(x) = sec^2(x)\cdot D_x(x)}$

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

The derivative of a sum of two or more functions is the sum of the derivatives of each function

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

The derivative of the constant function ($1$) is equal to zero

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

The derivative of the linear function is equal to $1$

$1\sec\left(x+1\right)^2$

Any expression multiplied by $1$ is equal to itself

$\sec\left(x+1\right)^2$
4

The derivative of the linear function is equal to $1$

$\sec\left(x+1\right)^2$

$\sec\left(x+1\right)^2$

##  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 tan(x+1) using the quotient ruleFind derivative of tan(x+1) using logarithmic differentiationFind derivative of tan(x+1) 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:

Product Rule of differentiation

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