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

The derivative of (x^2-1)/(sqrt(x^3)) is (4xsqrt(x^2)-3(x^2-1))/(2x^{5/2)}

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

The first derivative of (x^2-1)/(sqrt(x^3)) is (4xsqrt(x^2)-3(x^2-1))/(2x^{5/2)}

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derivative of

\frac{x ^{2} - 1}{x ^{3}}

\frac{4 x x ^{2} - 3 ( x ^{2} - 1 )}{2 x ^{\frac{5}{2}}}

Solution steps

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

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

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

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

Simplify

\frac{2 x x ^{3} - \frac{3 x}{2} ( x ^{2} - 1 )}{( x ^{3} ) ^{2}} : \frac{4 x x ^{2} - 3 ( x ^{2} - 1 )}{2 x ^{\frac{5}{2}}}

= \frac{4 x x ^{2} - 3 ( x ^{2} - 1 )}{2 x ^{\frac{5}{2}}}

\frac{d v}{d t} = 2.1 - \frac{7 v}{2180}, v (0) = 0

f (x) = - 2 x^{3}, at x = 2

\frac{d}{d z} (\frac{z ^{2}}{( z - 2 i ) ^{2}})

\frac{d}{d x} ((1 + 2 sin (x)) sin (x))

\int \frac{x arctan ( x )}{( 1 + x ^{2} ) ^{2}} d x

What is the derivative of (x^2-1)/(sqrt(x^3)) ?
The derivative of (x^2-1)/(sqrt(x^3)) is (4xsqrt(x^2)-3(x^2-1))/(2x^{5/2)}
What is the first derivative of (x^2-1)/(sqrt(x^3)) ?
The first derivative of (x^2-1)/(sqrt(x^3)) is (4xsqrt(x^2)-3(x^2-1))/(2x^{5/2)}