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Popular Calculus >

derivative of (x^2/(x^3))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of e^x(x^2+1)(x+4)

d er i v a t i v e e^{x} (x^{2} + 1) (x + 4)

area y=-x,y=-x^2+ex

a re a y = - x, y = - x^{2} + e x

parity (csc(3x))/(x^3)

p a r i t y \frac{csc ( 3 x )}{x ^{3}}

integral of (e^{-x})/(x^3)

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

integral of 9tan^3(2x)sec^5(2x)

\int 9 tan^{3} (2 x) sec^{5} (2 x) d x

Frequently Asked Questions (FAQ)

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