What is the derivative of f(x)=(1/(x-3))^2 ?

The derivative of f(x)=(1/(x-3))^2 is -2/((x-3)^3)

What is the first derivative of f(x)=(1/(x-3))^2 ?

The first derivative of f(x)=(1/(x-3))^2 is -2/((x-3)^3)

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derivative of

f (x) = (\frac{1}{x - 3})^{2}

- \frac{2}{( x - 3 ) ^{3}}

Solution steps

\frac{d}{d x} ((\frac{1}{x - 3})^{2})

Apply the chain rule:

2 \cdot \frac{1}{x - 3} \frac{d}{d x} (\frac{1}{x - 3})

= 2 \cdot \frac{1}{x - 3} \frac{d}{d x} (\frac{1}{x - 3})

\frac{d}{d x} (\frac{1}{x - 3}) = - \frac{1}{( x - 3 ) ^{2}}

= 2 \cdot \frac{1}{x - 3} (- \frac{1}{( x - 3 ) ^{2}})

Simplify

2 \cdot \frac{1}{x - 3} (- \frac{1}{( x - 3 ) ^{2}}) : - \frac{2}{( x - 3 ) ^{3}}

= - \frac{2}{( x - 3 ) ^{3}}

x^{3} + 2 x^{2} + 1

\int \frac{x ^{3}}{3} - \frac{3}{x ^{3}} d x

\int \frac{x ^{2}}{x ^{2} + 9} d x

x \to - π - lim (csc (x))

x^{^{''}} + 2 x^{^{'}} + 2 = 0

What is the derivative of f(x)=(1/(x-3))^2 ?
The derivative of f(x)=(1/(x-3))^2 is -2/((x-3)^3)
What is the first derivative of f(x)=(1/(x-3))^2 ?
The first derivative of f(x)=(1/(x-3))^2 is -2/((x-3)^3)