We have an answer to "Please, find the derivative of 1x2."

High School
Calculus and Analysis
Calculus 1
Derivatives

kramtus51

Answered question

2021-12-17

Please, find the derivative of

\frac{1}{x^{2}}

Answer & Explanation

Esther Phillips

Beginner2021-12-18Added 34 answers

Let

y = \frac{1}{x^{2}}

which is the same as

x^{- 2}

\frac{d y}{d x} = - 2 \times x^{- 2 - 1} = - 2 x^{- 3}

\frac{d y}{d x} = - \frac{2}{x^{- 3}}

Alex Sheppard

Beginner2021-12-19Added 36 answers

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \times x^{a - 1}

- 2 x^{- 2 - 1}

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

RizerMix

Expert2021-12-29Added 656 answers

Use the formula:
$D \frac{f (x)}{g (x)} = \frac{f^{'} (x) g (x) - f (x) g^{'} (x)}{g^{2} (x)}$
If f(x)=1, you have f'(x)=0 and you get:
$D \frac{1}{g (x)} = \frac{- g^{'} (x)}{g^{2} (x)}$
Since $g (x) = x^{2}$ , you get $g^{'} (x) = 2 x$ . Thus,
$\frac{- g^{'} (x)}{g^{2} (x)} = - \frac{2 x}{x^{2}} = - \frac{2}{x^{3}}$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f (x, y) = x^{3} - 6 x y + 8 y^{3}$
$\frac{1}{\sec (x)}$ in derivative?
What is the derivative of $\ln (x + 1)$ ?
What is the limit of $e^{- x}$ as $x \to \infty$ ?
What is the derivative of $f (x) = 5^{\ln x}$ ?
What is the derivative of $e^{- 2 x}$ ?
How to find $lim \frac{e^{t} - 1}{t}$ as $t \to 0$ using l'Hospital's Rule?
What is the integral of $\sqrt{9 - x^{2}}$ ?
What is the derivative of $f (x) = \ln [x^{9} {(x + 3)}^{6} {(x^{2} + 7)}^{5}]$ ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of $y = e^{5 x}$ ?
How to evaluate the limit $\frac{\sin (5 x)}{x}$ as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of $- 5 e^{x - 1}$ ?
How to evaluate: indefinite integral $\frac{1 + x}{1 + x^{2}} d x$ ?

Didn't find what you were looking for?