What is (\partial)/(\partial x)((3x^5-7)/(4x)) ?

The answer to (\partial)/(\partial x)((3x^5-7)/(4x)) is (12x^5+7)/(4x^2)

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(\partial)/(\partial x)((3x^5-7)/(4x))

\frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{4 x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{4 x})

Take the constant out:

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

= \frac{1}{4} \frac{\partial}{\partial x} (\frac{3 x ^{5} - 7}{x})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{\partial}{\partial x} ( 3 x ^{5} - 7 ) x - \frac{\partial}{\partial x} ( x ) ( 3 x ^{5} - 7 )}{x ^{2}}

\frac{\partial}{\partial x} (3 x^{5} - 7) = 15 x^{4}

\frac{\partial}{\partial x} (x) = 1

= \frac{1}{4} \cdot \frac{15 x ^{4} x - 1 \cdot ( 3 x ^{5} - 7 )}{x ^{2}}

Simplify

\frac{1}{4} \cdot \frac{15 x ^{4} x - 1 \cdot ( 3 x ^{5} - 7 )}{x ^{2}} : \frac{12 x ^{5} + 7}{4 x ^{2}}

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

What is (\partial)/(\partial x)((3x^5-7)/(4x)) ?
The answer to (\partial)/(\partial x)((3x^5-7)/(4x)) is (12x^5+7)/(4x^2)