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Find the derivative using the product rule $\frac{d}{dx}\left(x\sqrt{x^2-1}\right)$

Step-by-step Solution

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Final Answer

$\frac{2x^2-1}{\sqrt{x^2-1}}$
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Step-by-step Solution

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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\sqrt{x^2-1}$

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

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

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(x(x^2-1)^1/2). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{x^2-1}. 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

$\frac{2x^2-1}{\sqrt{x^2-1}}$

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

Find the derivativeFind derivative of x(x^2-1)^0.5 using the quotient ruleFind derivative of x(x^2-1)^0.5 using logarithmic differentiationFind derivative of x(x^2-1)^0.5 using the definition

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Function Plot

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

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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

How to improve your answer:

Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

Used Formulas

5. See formulas

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