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Find the implicit derivative of $\sqrt{\frac{x^2+y^2}{x^2}}+1=-x+c$

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Solution

Final answer to the problem

$\frac{\left(2x+2y\cdot y^{\prime}\right)x^2+2\left(-x^2-y^2\right)x}{2x^{4}}\sqrt{\frac{x^2}{x^2+y^2}}=-1$
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Step-by-step Solution

How should I solve this problem?

  • Solve by implicit differentiation
  • Find the derivative using the definition
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
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1

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

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

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

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Find the implicit derivative of ((x^2+y^2)/(x^2))^(1/2)+1=-x+c. 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 the linear function times a constant, is equal to the constant.

Final answer to the problem

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

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

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5
6
7
8
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

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