Find the derivative of y^2xy*-4+x^2=1

\frac{d}{dx}\left(x^2+y^2-4xy=1\right)

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$2x-4y+0=0$

Step by step solution

Problem

$\frac{d}{dx}\left(x^2+y^2-4xy=1\right)$
1

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

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

The derivative of the constant function is equal to zero

$\frac{d}{dx}\left(-4y\cdot x+y^2+x^2\right)=0$
3

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(-4y\cdot x\right)+\frac{d}{dx}\left(y^2\right)+\frac{d}{dx}\left(x^2\right)=0$
4

The derivative of the constant function is equal to zero

$\frac{d}{dx}\left(-4y\cdot x\right)+0+\frac{d}{dx}\left(x^2\right)=0$
5

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=-4x$ and $g=y$

$0+\frac{d}{dx}\left(x^2\right)-4x\frac{d}{dx}\left(y\right)+y\frac{d}{dx}\left(-4x\right)=0$
6

The derivative of the constant function is equal to zero

$0+\frac{d}{dx}\left(x^2\right)+0\left(-4\right)x+y\frac{d}{dx}\left(-4x\right)=0$
7

Any expression multiplied by $0$ is equal to $0$

$0+\frac{d}{dx}\left(x^2\right)+0+y\frac{d}{dx}\left(-4x\right)=0$
8

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$0+\frac{d}{dx}\left(x^2\right)+0-4y\frac{d}{dx}\left(x\right)=0$
9

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

$0+\frac{d}{dx}\left(x^2\right)+0+1\left(-4\right)y=0$
10

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

$0+2x+0+1\left(-4\right)y=0$
11

Add the values $0$ and $0$

$2x+1\left(-4\right)y+0=0$
12

Multiply $-4$ times $1$

$2x-4y+0=0$

$2x-4y+0=0$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

Main topic:

Differential calculus

0.26 seconds

110