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Find the derivative of $\arccos\left(e^x\right)$

Step-by-step Solution

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Final Answer

$\frac{-e^x}{\sqrt{1-e^{2x}}}$
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Step-by-step Solution

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Taking the derivative of arccosine

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

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

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of arccos(e^x). Taking the derivative of arccosine. Simplify \left(e^x\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals x and n equals 2. Applying the derivative of the exponential function. Multiplying the fraction by e^x.

Final Answer

$\frac{-e^x}{\sqrt{1-e^{2x}}}$

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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 arccos(e^x) using the product ruleFind derivative of arccos(e^x) using the quotient ruleFind derivative of arccos(e^x) using logarithmic differentiation

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Function Plot

Plotting: $\frac{-e^x}{\sqrt{1-e^{2x}}}$

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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

How to improve your answer:

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.

Used Formulas

1. See formulas

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