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# Find the derivative of $\left(9-x^2\right)^{-\frac{1}{2}}$

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##  Final answer to the problem

$\frac{x}{\sqrt{\left(9-x^2\right)^{3}}}$
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##  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
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1

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

$-\frac{1}{2}\left(9-x^2\right)^{-\frac{3}{2}}\frac{d}{dx}\left(9-x^2\right)$

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$-\frac{1}{2}\left(9-x^2\right)^{-\frac{3}{2}}\frac{d}{dx}\left(9-x^2\right)$

Learn how to solve problems step by step online. Find the derivative of (9-x^2)^(-1/2). 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. The derivative of the constant function (9) is equal to zero. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

##  Final answer to the problem

$\frac{x}{\sqrt{\left(9-x^2\right)^{3}}}$

##  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

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1
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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