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

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

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

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

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derivative of

\frac{( 2 x + 1 )}{x ^{3}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{1}^{2} x^{2} + \frac{1}{4 x ^{2}} d x

f (x) = 1 - e^{- x}

- 5 ln (sin (x))

\int \frac{4}{9 - 9 x ^{2}} d x

x^{2} + 9 (- 5.34)

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