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Find the derivative of $\sin\left(\frac{x^2}{5}\right)$

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Solution

Formulas

Videos

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

Calculus - How to use the chain rule with trigonometric functions, g(x) = sin(x^2)

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

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

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

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

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

Calculus - Using the power rule of logarithms to take the derivative of a natural log, d(ln(x^2))/dx

https://www.youtube.com/watch?v=JIq0y4ST7tc

Function Plot

Plotting: $\frac{2}{5}x\cos\left(\frac{x^2}{5}\right)$

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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
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

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

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

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

$\frac{d}{dx}\left(\arcsin\left(4x^2\right)\right)$

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

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

Find the derivative

$\frac{d}{dx}\left(\sqrt[4]{x}\right)$

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 (3)

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