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

Step-by-step Solution

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asinh
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Final Answer

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

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

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

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

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 d/dx(tan(x+1)) using the product ruleFind d/dx(tan(x+1)) using the quotient ruleFind d/dx(tan(x+1)) using logarithmic differentiationFind d/dx(tan(x+1)) using the definition
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Got a different answer? Verify it!

Go!
1
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7
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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

How to improve your answer:

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

Main topic:

Differential Calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.03 s