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Step-by-step Solution

Find the derivative of $\tan\left(x+1\right)$

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Final Answer

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

Problem to solve:

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

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

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

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

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

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

$\sec\left(x+1\right)^2\left(\frac{d}{dx}\left(x\right)+0\right)$

$x+0=x$, where $x$ is any expression

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

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

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

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 $1$

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

Final Answer

$\sec\left(x+1\right)^2$
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Got another answer? Verify it!

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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

Tips on how to improve your answer:

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

Main topic:

Differential Calculus

Related Formulas:

4. See formulas

Time to solve it:

~ 0.03 s