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# Find the implicit derivative $\frac{d}{dx}\left(x^2+y^2=25\right)$

## Step-by-step Solution

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asinh
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###  Videos

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

Problem to solve:

$\frac{d}{dx}\left(x^2+y^2=25\right)$

Specify the solving method

1

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

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(25\right)$
2

The derivative of the constant function ($25$) is equal to zero

$\frac{d}{dx}\left(x^2+y^2\right)=0$
3 Try to guess Step 3. Or become premium for the price of a latte.
4

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{d}{dx}\left(x^2\right)+2y\frac{d}{dx}\left(y\right)=0$

$2\cdot 1y$

Any expression multiplied by $1$ is equal to itself

$2y$
5

The derivative of the linear function is equal to $1$

$\frac{d}{dx}\left(x^2\right)+2y\cdot y^{\prime}=0$
6 Try to guess Step 6. Or become premium for the price of a latte.
7

Isolate $2y\cdot y^{\prime}$

$2y\cdot y^{\prime}=0-2x$
8

$x+0=x$, where $x$ is any expression

$2y\cdot y^{\prime}=-2x$
9 Try to guess Step 9. Or become premium for the price of a latte.
10

Simplifying the quotients

$y\cdot y^{\prime}=\frac{-2x}{2}$
11

Take $\frac{-2}{2}$ out of the fraction

$y\cdot y^{\prime}=-x$
12 Try to guess Step 12. Or become premium for the price of a latte.
13

Simplifying the quotients

$y^{\prime}=\frac{-x}{y}$

$y^{\prime}=\frac{-x}{y}$

SnapXam A2

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

### Main topic:

Implicit Differentiation

~ 0.11 s

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