What is the derivative of (3(7x^2-2x+6))/(4x^{5/2)} ?

The derivative of (3(7x^2-2x+6))/(4x^{5/2)} is (3(-7x^2+6x-30))/(8x^{7/2)}

What is the first derivative of (3(7x^2-2x+6))/(4x^{5/2)} ?

The first derivative of (3(7x^2-2x+6))/(4x^{5/2)} is (3(-7x^2+6x-30))/(8x^{7/2)}

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derivative of

\frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

\frac{3 ( - 7 x ^{2} + 6 x - 30 )}{8 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{3}{4} \frac{d}{d x} (\frac{7 x ^{2} - 2 x + 6}{x ^{\frac{5}{2}}})

Apply the Quotient Rule:

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

= \frac{3}{4} \cdot \frac{\frac{d}{d x} ( 7 x ^{2} - 2 x + 6 ) x ^{\frac{5}{2}} - \frac{d}{d x} ( x ^{\frac{5}{2}} ) ( 7 x ^{2} - 2 x + 6 )}{( x ^{\frac{5}{2}} ) ^{2}}

\frac{d}{d x} (7 x^{2} - 2 x + 6) = 14 x - 2

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

= \frac{3}{4} \cdot \frac{( 14 x - 2 ) x ^{\frac{5}{2}} - \frac{5 x ^{\frac{3}{2}}}{2} ( 7 x ^{2} - 2 x + 6 )}{( x ^{\frac{5}{2}} ) ^{2}}

Simplify

\frac{3}{4} \cdot \frac{( 14 x - 2 ) x ^{\frac{5}{2}} - \frac{5 x ^{\frac{3}{2}}}{2} ( 7 x ^{2} - 2 x + 6 )}{( x ^{\frac{5}{2}} ) ^{2}} : \frac{3 ( - 7 x ^{2} + 6 x - 30 )}{8 x ^{\frac{7}{2}}}

= \frac{3 ( - 7 x ^{2} + 6 x - 30 )}{8 x ^{\frac{7}{2}}}

\frac{\partial}{\partial x} (x y e^{z})

y = 2 sin (2 x)

\frac{\partial}{\partial x} (x y e^{2})

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

\int \frac{x ^{2} - x + 13}{( x + 1 ) ( x ^{2} + 4 )} d x

What is the derivative of (3(7x^2-2x+6))/(4x^{5/2)} ?
The derivative of (3(7x^2-2x+6))/(4x^{5/2)} is (3(-7x^2+6x-30))/(8x^{7/2)}
What is the first derivative of (3(7x^2-2x+6))/(4x^{5/2)} ?
The first derivative of (3(7x^2-2x+6))/(4x^{5/2)} is (3(-7x^2+6x-30))/(8x^{7/2)}