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# Find the derivative of $\sec\left(x+1\right)^2$

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##  Final answer to the problem

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

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• Find the derivative using the definition
• Find the derivative using the product rule
• Find the derivative using the quotient rule
• Find the derivative using logarithmic differentiation
• Find the derivative
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
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1

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

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

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

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

Learn how to solve differential calculus problems step by step online. Find the derivative of sec(x+1)^2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Any expression to the power of 1 is equal to that same expression. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x). When multiplying two powers that have the same base (\sec\left(x+1\right)), you can add the exponents.

##  Final answer to the problem

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

##  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

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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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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