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Find the implicit derivative $\frac{d}{dx}\left(\arctan\left(x+3y\right)\right)=x^4$

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Solution

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Final answer to the problem

$\frac{1}{1+\left(x+3y\right)^2}\left(1+3y^{\prime}\right)=x^4$
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Learn how to solve inverse trigonometric functions differentiation problems step by step online. Find the implicit derivative d/dx(arctan(x+3y))=x^4. Taking the derivative of arctangent. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.

Final answer to the problem

$\frac{1}{1+\left(x+3y\right)^2}\left(1+3y^{\prime}\right)=x^4$

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Function Plot

Plotting: $\frac{1}{1+\left(x+3y\right)^2}\left(1+3y^{\prime}\right)=x^4$

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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:

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Main Topic: Inverse trigonometric functions differentiation

Describes how to find the derivative of the inverse of the trigonometric functions sine, cosine, tangent, etc.

Used Formulas

See formulas (4)

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