What is the derivative of ((3x^7-7x^2+113)/((5x^3))) ?

The derivative of ((3x^7-7x^2+113)/((5x^3))) is (12x^7+7x^2-339)/(5x^4)

What is the first derivative of ((3x^7-7x^2+113)/((5x^3))) ?

The first derivative of ((3x^7-7x^2+113)/((5x^3))) is (12x^7+7x^2-339)/(5x^4)

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\frac{d}{d x} (\frac{( 3 x ^{7} - 7 x ^{2} + 113 )}{( 5 x ^{3} )})

\frac{12 x ^{7} + 7 x ^{2} - 339}{5 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{( 3 x ^{7} - 7 x ^{2} + 113 )}{( 5 x ^{3} )})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{3 x ^{7} - 7 x ^{2} + 113}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( 3 x ^{7} - 7 x ^{2} + 113 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 x ^{7} - 7 x ^{2} + 113 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 x^{7} - 7 x^{2} + 113) = 21 x^{6} - 14 x

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

= \frac{1}{5} \cdot \frac{( 21 x ^{6} - 14 x ) x ^{3} - 3 x ^{2} ( 3 x ^{7} - 7 x ^{2} + 113 )}{( x ^{3} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{( 21 x ^{6} - 14 x ) x ^{3} - 3 x ^{2} ( 3 x ^{7} - 7 x ^{2} + 113 )}{( x ^{3} ) ^{2}} : \frac{12 x ^{7} + 7 x ^{2} - 339}{5 x ^{4}}

= \frac{12 x ^{7} + 7 x ^{2} - 339}{5 x ^{4}}

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

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.2 y)

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

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} d x

\frac{\partial}{\partial x} (\frac{( x + y )}{x y})

What is the derivative of ((3x^7-7x^2+113)/((5x^3))) ?
The derivative of ((3x^7-7x^2+113)/((5x^3))) is (12x^7+7x^2-339)/(5x^4)
What is the first derivative of ((3x^7-7x^2+113)/((5x^3))) ?
The first derivative of ((3x^7-7x^2+113)/((5x^3))) is (12x^7+7x^2-339)/(5x^4)