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

The derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)

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

The first derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)

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derivative of

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

- \frac{3}{x ^{4}}

Solution steps

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

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

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

\frac{d}{d x} (x^{3} x^{2}) = 5 x^{4}

= \frac{2 x x ^{3} x ^{2} - 5 x ^{4} x ^{2}}{( x ^{3} x ^{2} ) ^{2}}

Simplify

\frac{2 x x ^{3} x ^{2} - 5 x ^{4} x ^{2}}{( x ^{3} x ^{2} ) ^{2}} : - \frac{3}{x ^{4}}

= - \frac{3}{x ^{4}}

\int \frac{1}{x x ^{2} - 81} d x

f (t) = t^{4} - 20 t^{3} + 112 t^{2}

f (x) = arccos (x) + x, at x = 0

t \frac{d y}{d t} + 18 y = \frac{1}{t}

f (x) = \frac{2 x - 1}{x + 3}, at x = 3

What is the derivative of f(x)=(x^2)/((x^3)(x^2)) ?
The derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)
What is the first derivative of f(x)=(x^2)/((x^3)(x^2)) ?
The first derivative of f(x)=(x^2)/((x^3)(x^2)) is -3/(x^4)