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Find the derivative $\frac{d}{dx}\left(\arctan\left(x^2y\right)-x-xy^2\right)$ using the sum rule

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Solving: $\frac{d}{dx}\left(\arctan\left(x^2y\right)-x-xy^2\right)$
Solve instead: $\frac{dy}{dx}\left(\arctan\left(x^2y\right)-x-xy^2\right)$

Solution

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Final answer to the problem

$\frac{2yx}{1+x^{4}y^2}-1-y^2$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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The derivative of a sum of two or more functions is the sum of the derivatives of each function

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

Learn how to solve sum rule of differentiation problems step by step online.

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

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(arctan(x^2y)-x-xy^2) using the sum rule. 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. 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

$\frac{2yx}{1+x^{4}y^2}-1-y^2$

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Plotting: $\frac{2yx}{1+x^{4}y^2}-1-y^2$

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(◻)
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◻/◻
/
÷
◻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

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

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

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

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

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

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

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

Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

See formulas (5)

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