ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Find the implicit derivative $\frac{d}{dx}\left(2x^2+yz-y^3z^4+\sqrt{x^2+y^2}=5xy^5\right)$

Go!
Symbolic mode
Text mode
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

##  Final answer to the problem

$4x+zy^{\prime}-3y^{2}y^{\prime}z^4+\frac{1}{2\sqrt{x^2+y^2}}\left(2x+2y\cdot y^{\prime}\right)=5\left(y^5+5xy^{4}y^{\prime}\right)$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

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

$\frac{d}{dx}\left(2x^2+yz-y^3z^4+\sqrt{x^2+y^2}\right)=\frac{d}{dx}\left(5xy^5\right)$

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

$\frac{d}{dx}\left(2x^2+yz-y^3z^4+\sqrt{x^2+y^2}\right)=\frac{d}{dx}\left(5xy^5\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative d/dx(2x^2+yz-y^3z^4(x^2+y^2)^(1/2)=5xy^5). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1.

##  Final answer to the problem

$4x+zy^{\prime}-3y^{2}y^{\prime}z^4+\frac{1}{2\sqrt{x^2+y^2}}\left(2x+2y\cdot y^{\prime}\right)=5\left(y^5+5xy^{4}y^{\prime}\right)$

##  Explore different ways to solve this problem

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

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

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.