What is the derivative of (12(3x^3-16)/(4x-x^4)) ?

The derivative of (12(3x^3-16)/(4x-x^4)) is (12(3x^6-40x^3+64))/((4x-x^4)^2)

What is the first derivative of (12(3x^3-16)/(4x-x^4)) ?

The first derivative of (12(3x^3-16)/(4x-x^4)) is (12(3x^6-40x^3+64))/((4x-x^4)^2)

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\frac{d}{d x} (\frac{12 ( 3 x ^{3} - 16 )}{4 x - x ^{4}})

\frac{12 ( 3 x ^{6} - 40 x ^{3} + 64 )}{( 4 x - x ^{4} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{12 ( 3 x ^{3} - 16 )}{4 x - x ^{4}})

Take the constant out:

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

= 12 \frac{d}{d x} (\frac{3 x ^{3} - 16}{4 x - x ^{4}})

Apply the Quotient Rule:

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

= 12 \cdot \frac{\frac{d}{d x} ( 3 x ^{3} - 16 ) ( 4 x - x ^{4} ) - \frac{d}{d x} ( 4 x - x ^{4} ) ( 3 x ^{3} - 16 )}{( 4 x - x ^{4} ) ^{2}}

\frac{d}{d x} (3 x^{3} - 16) = 9 x^{2}

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

= 12 \cdot \frac{9 x ^{2} ( 4 x - x ^{4} ) - ( 4 - 4 x ^{3} ) ( 3 x ^{3} - 16 )}{( 4 x - x ^{4} ) ^{2}}

Simplify

12 \cdot \frac{9 x ^{2} ( 4 x - x ^{4} ) - ( 4 - 4 x ^{3} ) ( 3 x ^{3} - 16 )}{( 4 x - x ^{4} ) ^{2}} : \frac{12 ( 3 x ^{6} - 40 x ^{3} + 64 )}{( 4 x - x ^{4} ) ^{2}}

= \frac{12 ( 3 x ^{6} - 40 x ^{3} + 64 )}{( 4 x - x ^{4} ) ^{2}}

\int p (p + 7)^{8} d p

\int t^{2} e^{- 3 t} d t

\int 2 y e^{2 x} d x

y^{^{''}} + 2 y^{^{'}} + y = 4 e^{- 1}

\frac{d}{d t} (tan (t + \frac{π}{4}))

What is the derivative of (12(3x^3-16)/(4x-x^4)) ?
The derivative of (12(3x^3-16)/(4x-x^4)) is (12(3x^6-40x^3+64))/((4x-x^4)^2)
What is the first derivative of (12(3x^3-16)/(4x-x^4)) ?
The first derivative of (12(3x^3-16)/(4x-x^4)) is (12(3x^6-40x^3+64))/((4x-x^4)^2)