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Find the derivative of $e^{\arctan\left(3x^2\right)}$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$\frac{6e^{\arctan\left(3x^2\right)}x}{1+9x^{4}}$
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Step-by-step Solution

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Learn how to solve power rule for derivatives problems step by step online. Find the derivative of e^arctan(3x^2). Applying the derivative of the exponential function. Taking the derivative of arctangent. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

Final answer to the problem

$\frac{6e^{\arctan\left(3x^2\right)}x}{1+9x^{4}}$

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Function Plot

Plotting: $\frac{6e^{\arctan\left(3x^2\right)}x}{1+9x^{4}}$

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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

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

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

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

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

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

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

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

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 (3)

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