What is the derivative of (5-x)/((4x^2+1)^3) ?

The derivative of (5-x)/((4x^2+1)^3) is -(-20x^2+120x+1)/((4x^2+1)^4)

What is the first derivative of (5-x)/((4x^2+1)^3) ?

The first derivative of (5-x)/((4x^2+1)^3) is -(-20x^2+120x+1)/((4x^2+1)^4)

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derivative of

\frac{5 - x}{( 4 x ^{2} + 1 ) ^{3}}

- \frac{- 20 x ^{2} + 120 x + 1}{( 4 x ^{2} + 1 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{5 - x}{( 4 x ^{2} + 1 ) ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 - x ) ( 4 x ^{2} + 1 ) ^{3} - \frac{d}{d x} ( ( 4 x ^{2} + 1 ) ^{3} ) ( 5 - x )}{( ( 4 x ^{2} + 1 ) ^{3} ) ^{2}}

\frac{d}{d x} (5 - x) = - 1

\frac{d}{d x} ((4 x^{2} + 1)^{3}) = 24 x (4 x^{2} + 1)^{2}

= \frac{( - 1 ) ( 4 x ^{2} + 1 ) ^{3} - 24 x ( 4 x ^{2} + 1 ) ^{2} ( 5 - x )}{( ( 4 x ^{2} + 1 ) ^{3} ) ^{2}}

Simplify

\frac{( - 1 ) ( 4 x ^{2} + 1 ) ^{3} - 24 x ( 4 x ^{2} + 1 ) ^{2} ( 5 - x )}{( ( 4 x ^{2} + 1 ) ^{3} ) ^{2}} : - \frac{- 20 x ^{2} + 120 x + 1}{( 4 x ^{2} + 1 ) ^{4}}

= - \frac{- 20 x ^{2} + 120 x + 1}{( 4 x ^{2} + 1 ) ^{4}}

\frac{d P}{d t} = 5 Pt, P (1) = 6

\frac{d}{d x} (\frac{( 7 - 5 x )}{cos ( x )})

\int (100 - x)^{2} d x

y = e^{- x^{2}}

f (x) = \frac{x ^{2} + 1}{x}

What is the derivative of (5-x)/((4x^2+1)^3) ?
The derivative of (5-x)/((4x^2+1)^3) is -(-20x^2+120x+1)/((4x^2+1)^4)
What is the first derivative of (5-x)/((4x^2+1)^3) ?
The first derivative of (5-x)/((4x^2+1)^3) is -(-20x^2+120x+1)/((4x^2+1)^4)