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Find the implicit derivative $\frac{d}{dx}\left(\mathrm{cosh}\left(x\right)\right)=\mathrm{sinh}\left(x\right)$

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Solution

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Final answer to the problem

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

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  • Find the derivative using the definition
  • Exact Differential Equation
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  • Find the derivative using the quotient rule
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1

Taking the derivative of hyperbolic cosine

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)\mathrm{sinh}\left(x\right)=\mathrm{sinh}\left(x\right)$

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Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(cosh(x))=sinh(x). Taking the derivative of hyperbolic cosine. The derivative of the linear function is equal to 1.

Final answer to the problem

$\mathrm{sinh}\left(x\right)=\mathrm{sinh}\left(x\right)$

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

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Go!
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
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:

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$\frac{d}{dx}\left(x^{\frac{2}{3}}+y^{\frac{2}{3}}=5\right)$

Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

Used Formulas

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