What is the derivative of (3x^7-7x+11/(2x^3)) ?

The derivative of (3x^7-7x+11/(2x^3)) is (12x^7+14x-33)/(2x^4)

What is the first derivative of (3x^7-7x+11/(2x^3)) ?

The first derivative of (3x^7-7x+11/(2x^3)) is (12x^7+14x-33)/(2x^4)

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\frac{d}{d x} (\frac{3 x ^{7} - 7 x + 11}{2 x ^{3}})

\frac{12 x ^{7} + 14 x - 33}{2 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{7} - 7 x + 11}{2 x ^{3}})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{3 x ^{7} - 7 x + 11}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 3 x ^{7} - 7 x + 11 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 x ^{7} - 7 x + 11 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 x^{7} - 7 x + 11) = 21 x^{6} - 7

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

= \frac{1}{2} \cdot \frac{( 21 x ^{6} - 7 ) x ^{3} - 3 x ^{2} ( 3 x ^{7} - 7 x + 11 )}{( x ^{3} ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( 21 x ^{6} - 7 ) x ^{3} - 3 x ^{2} ( 3 x ^{7} - 7 x + 11 )}{( x ^{3} ) ^{2}} : \frac{12 x ^{7} + 14 x - 33}{2 x ^{4}}

= \frac{12 x ^{7} + 14 x - 33}{2 x ^{4}}

What is the derivative of (3x^7-7x+11/(2x^3)) ?
The derivative of (3x^7-7x+11/(2x^3)) is (12x^7+14x-33)/(2x^4)
What is the first derivative of (3x^7-7x+11/(2x^3)) ?
The first derivative of (3x^7-7x+11/(2x^3)) is (12x^7+14x-33)/(2x^4)