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

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

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

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

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derivative of

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

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

Solution steps

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

\frac{d}{d x} (3 x^{2} + 1) = 6 x

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

= \frac{6 x x ^{\frac{3}{2}} - \frac{3 x ^{\frac{1}{2}}}{2} ( 3 x ^{2} + 1 )}{( x ^{\frac{3}{2}} ) ^{2}}

Simplify

\frac{6 x x ^{\frac{3}{2}} - \frac{3 x ^{\frac{1}{2}}}{2} ( 3 x ^{2} + 1 )}{( x ^{\frac{3}{2}} ) ^{2}} : \frac{3 ( x ^{2} - 1 )}{2 x ^{\frac{5}{2}}}

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

\int e^{i 8 x} cos (4 x) d x

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

\int 3 x^{2} x^{3} - 5 d x

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

\int \frac{6 x - 15}{x ^{2} - 3 x} d x

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