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Find the derivative of $\cos\left(\mathrm{sinh}\left(\sqrt[4]{x}\right)\right)^3$

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Solution

Formulas

Videos

Derivatives of sec(x) and csc(x) | Derivative rules | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=TDJ5nXWEkWM

Calculus - Learn how to take derivative using quotient rule by simplifying first, f(x)=x(1- 4/(x+3))

https://www.youtube.com/watch?v=Mqjiw5Ax_4w

Finding the derivative square root x over x, using power rule

https://www.youtube.com/watch?v=oR6DDJ-rvbQ

How to find the derivative of square root and cube root using power rule

https://www.youtube.com/watch?v=ge_6J6KIm4I

Definite integral of rational function | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=4WJUEXIksH0

Worked example: Derivatives of sin(x) and cos(x) | Derivative rules | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=Iur13MNO0Ro

Function Plot

Plotting: $\frac{-3\cos\left(\mathrm{sinh}\left(\sqrt[4]{x}\right)\right)^{2}\sin\left(\mathrm{sinh}\left(\sqrt[4]{x}\right)\right)\mathrm{cosh}\left(\sqrt[4]{x}\right)}{4\sqrt[4]{x^{3}}}$

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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
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

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

$\frac{d}{dx}\left(\sqrt{\sin\left(x\right)}\right)$

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

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

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

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

$\frac{d}{dx}\left(\cosh\left(x^5\right)\right)$

Main Topic: Power Rule for Derivatives

The power rule is used to differentiate functions of the form f(x)=x^a, when a is a real number.

Used Formulas

See formulas (2)

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