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Find the implicit derivative $\frac{d}{dx}\left(x^2+y^2=10-5xy\right)$

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Solution

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Final answer to the problem

$2x+2y\cdot y^{\prime}=-5\left(y+xy^{\prime}\right)$
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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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Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(10-5xy\right)$

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(10-5xy\right)$

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Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(x^2+y^2=10-5xy). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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

$2x+2y\cdot y^{\prime}=-5\left(y+xy^{\prime}\right)$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Plotting: $2x+2y\cdot y^{\prime}=-5\left(y+xy^{\prime}\right)$

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0
a
b
c
d
f
g
m
n
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v
w
x
y
z
.
(◻)
+
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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

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Main Topic: Implicit Differentiation

Implicit differentiation makes use of the chain rule to differentiate implicitly defined functions. For differentiating an implicit function y(x), defined by an equation R(x, y) = 0, it is not generally possible to solve it explicitly for y(x) and then differentiate. Instead, one can differentiate R(x, y) with respect to x and y and then solve a linear equation in dy/dx for getting explicitly the derivative in terms of x and y.

Used Formulas

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