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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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