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

The derivative of f(x)=(x^2+3)/(x^2) is -6/(x^3)

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

The first derivative of f(x)=(x^2+3)/(x^2) is -6/(x^3)

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derivative of

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

- \frac{6}{x ^{3}}

Solution steps

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

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

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

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

Simplify

\frac{2 x x ^{2} - 2 x ( x ^{2} + 3 )}{( x ^{2} ) ^{2}} : - \frac{6}{x ^{3}}

= - \frac{6}{x ^{3}}

y = cos^{2} (3 x - 1)

x \to 0 - lim (\frac{8}{5 x ^{\frac{1}{2}}})

(5.4) (7.7)

\int \frac{x ^{2}}{( 15 + 6 x - 9 x ^{2} ) ^{\frac{3}{2}}} d x

f (x) = x + 1, at x = 0

What is the derivative of f(x)=(x^2+3)/(x^2) ?
The derivative of f(x)=(x^2+3)/(x^2) is -6/(x^3)
What is the first derivative of f(x)=(x^2+3)/(x^2) ?
The first derivative of f(x)=(x^2+3)/(x^2) is -6/(x^3)