Calculators AI Whiteboard Worksheets & Tests
Book solutions
Algebra Baldor
Go Premium Topics

Find the implicit derivative $\frac{d}{dx}\left(y=\sqrt{x^2-1}\right)$

Step-by-step Solution

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
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

Solution

Formulas

Videos

Final answer to the problem

$y^{\prime}=\frac{x}{\sqrt{x^2-1}}$
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
  • Load more...
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

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

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

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

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

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

Final answer to the problem

$y^{\prime}=\frac{x}{\sqrt{x^2-1}}$

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

Help us improve with your feedback!

Function Plot

Plotting: $y^{\prime}=\frac{x}{\sqrt{x^2-1}}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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
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

How to improve your answer:

Similar Problems Solved

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(xy+2x+3x^2=4\right)$

Find the derivative

$\frac{d}{dx}\left(x^{\frac{2}{3}}+y^{\frac{2}{3}}=5\right)$

Find the derivative

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

Find the derivative

$\frac{d}{dx}\left(x^3-3x^2y+2xy^2=12\right)$

Find the derivative

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

Find the derivative

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

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.

Used Formulas

See formulas (4)

Related Topics

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account