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Find the derivative of $c\mathrm{cosh}\left(\frac{x}{c}\right)$

Step-by-step Solution

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Solution

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Final answer to the problem

$\mathrm{sinh}\left(\frac{x}{c}\right)$
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Step-by-step Solution

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  • Choose an option
  • 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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The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$c\frac{d}{dx}\left(\mathrm{cosh}\left(\frac{x}{c}\right)\right)$

Learn how to solve basic differentiation rules problems step by step online.

$c\frac{d}{dx}\left(\mathrm{cosh}\left(\frac{x}{c}\right)\right)$

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Unlock the first 3 steps of this solution

Learn how to solve basic differentiation rules problems step by step online. Find the derivative of ccosh(x/c). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Taking the derivative of hyperbolic cosine. The derivative of a function multiplied by a constant (\frac{1}{c}) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1.

Final answer to the problem

$\mathrm{sinh}\left(\frac{x}{c}\right)$

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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

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Function Plot

Plotting: $\mathrm{sinh}\left(\frac{x}{c}\right)$

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1
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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
D□x
∫
∫◻
|◻|
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:

Similar Problems Solved

$\frac{d}{dx}\left(\ln\left(\mathrm{sech}\left(3x+8\right)\right)\right)$

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

$\frac{d}{dx}\left(\sinh^2\left(3x\right)\right)$

$\frac{d}{dx}\left(ln\:\left(\tan^{-1}\left(sen\:h\:\left(x\right)\right)\right)\right)$

$\frac{d}{dx}\left(\cosh^2\left(3x\right)\right)$

Main Topic: Basic Differentiation Rules

Some differentiation rules are very easy to remember and use. These are the basic ones: constant rule, sum rule, product rule and quotient rule.

Used Formulas

See formulas (3)

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