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

The derivative of (2x-5/((x^2+4)^3)) is (2(-5x^2+15x+4))/((x^2+4)^4)

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

The first derivative of (2x-5/((x^2+4)^3)) is (2(-5x^2+15x+4))/((x^2+4)^4)

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

\frac{2 ( - 5 x ^{2} + 15 x + 4 )}{( x ^{2} + 4 ) ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x - 5) = 2

\frac{d}{d x} ((x^{2} + 4)^{3}) = 6 x (x^{2} + 4)^{2}

= \frac{2 ( x ^{2} + 4 ) ^{3} - 6 x ( x ^{2} + 4 ) ^{2} ( 2 x - 5 )}{( ( x ^{2} + 4 ) ^{3} ) ^{2}}

Simplify

\frac{2 ( x ^{2} + 4 ) ^{3} - 6 x ( x ^{2} + 4 ) ^{2} ( 2 x - 5 )}{( ( x ^{2} + 4 ) ^{3} ) ^{2}} : \frac{2 ( - 5 x ^{2} + 15 x + 4 )}{( x ^{2} + 4 ) ^{4}}

= \frac{2 ( - 5 x ^{2} + 15 x + 4 )}{( x ^{2} + 4 ) ^{4}}

What is the derivative of (2x-5/((x^2+4)^3)) ?
The derivative of (2x-5/((x^2+4)^3)) is (2(-5x^2+15x+4))/((x^2+4)^4)
What is the first derivative of (2x-5/((x^2+4)^3)) ?
The first derivative of (2x-5/((x^2+4)^3)) is (2(-5x^2+15x+4))/((x^2+4)^4)