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Find the derivative $\frac{d}{dx}\left(\frac{-1}{\left(x-6\right)^2}\right)$

Step-by-step Solution

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Final Answer

$\frac{2}{\left(x-6\right)^{3}}$
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Step-by-step Solution

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Apply the quotient rule for differentiation, which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{\frac{d}{dx}\left(-1\right)\left(x-6\right)^2-\left(-1\right)\frac{d}{dx}\left(\left(x-6\right)^2\right)}{\left(\left(x-6\right)^2\right)^2}$

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$\frac{\frac{d}{dx}\left(-1\right)\left(x-6\right)^2-\left(-1\right)\frac{d}{dx}\left(\left(x-6\right)^2\right)}{\left(\left(x-6\right)^2\right)^2}$

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Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(-1/((x-6)^2)). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Multiply -1 times -1. Simplify \left(\left(x-6\right)^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2. The derivative of the constant function (-1) is equal to zero.

Final Answer

$\frac{2}{\left(x-6\right)^{3}}$

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

Find the derivativeFind derivative of -1/((x-6)^2) using the product ruleFind derivative of -1/((x-6)^2) using the quotient ruleFind derivative of -1/((x-6)^2) using logarithmic differentiationFind derivative of -1/((x-6)^2) using the definition

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Function Plot

Plotting: $\frac{2}{\left(x-6\right)^{3}}$

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a
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g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

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