What is the derivative of ((x-4(x^2+4x+16))/(x^3)) ?

The derivative of ((x-4(x^2+4x+16))/(x^3)) is (192)/(x^4)

What is the first derivative of ((x-4(x^2+4x+16))/(x^3)) ?

The first derivative of ((x-4(x^2+4x+16))/(x^3)) is (192)/(x^4)

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\frac{d}{d x} (\frac{( x - 4 ) ( x ^{2} + 4 x + 16 )}{x ^{3}})

\frac{192}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{( x - 4 ) ( x ^{2} + 4 x + 16 )}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( x - 4 ) ( x ^{2} + 4 x + 16 ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x - 4 ) ( x ^{2} + 4 x + 16 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} ((x - 4) (x^{2} + 4 x + 16)) = 3 x^{2}

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

= \frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x - 4 ) ( x ^{2} + 4 x + 16 )}{( x ^{3} ) ^{2}}

Simplify

\frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x - 4 ) ( x ^{2} + 4 x + 16 )}{( x ^{3} ) ^{2}} : \frac{192}{x ^{4}}

= \frac{192}{x ^{4}}

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

x \to 2 lim (x^{3} - 5 x^{2} + 4)

\int \frac{3 x ^{2}}{16 - x ^{2}} d x

y^{^{''}} + 2 y^{^{'}} + y = e^{t}

y^{^{'''}} - 3 y^{^{''}} + y^{^{'}} - 3 y = 0

What is the derivative of ((x-4(x^2+4x+16))/(x^3)) ?
The derivative of ((x-4(x^2+4x+16))/(x^3)) is (192)/(x^4)
What is the first derivative of ((x-4(x^2+4x+16))/(x^3)) ?
The first derivative of ((x-4(x^2+4x+16))/(x^3)) is (192)/(x^4)