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# Find the implicit derivative $\frac{d}{dx}\left(x^2+y^2=16\right)$

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## Final Answer

$y^{\prime}=\frac{-x}{y}$
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## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(x^2+y^2=16\right)$
1

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

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(16\right)$

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

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(16\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(x^2+y^2=16). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the constant function (16) is equal to zero. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

## Final Answer

$y^{\prime}=\frac{-x}{y}$
SnapXam A2
Answer Assistant

Go!
1
2
3
4
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
Dx
|◻|
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

### Tips on how to improve your answer:

$\frac{d}{dx}\left(x^2+y^2=16\right)$

### Main topic:

Implicit Differentiation

~ 0.05 s