What is the derivative of (x^6+3x^2+50)/(x^2+1) ?

The derivative of (x^6+3x^2+50)/(x^2+1) is (4x^7+6x^5-94x)/((x^2+1)^2)

What is the first derivative of (x^6+3x^2+50)/(x^2+1) ?

The first derivative of (x^6+3x^2+50)/(x^2+1) is (4x^7+6x^5-94x)/((x^2+1)^2)

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derivative of

\frac{x ^{6} + 3 x ^{2} + 50}{x ^{2} + 1}

\frac{4 x ^{7} + 6 x ^{5} - 94 x}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{6} + 3 x ^{2} + 50}{x ^{2} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{6} + 3 x ^{2} + 50 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( x ^{6} + 3 x ^{2} + 50 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (x^{6} + 3 x^{2} + 50) = 6 x^{5} + 6 x

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

= \frac{( 6 x ^{5} + 6 x ) ( x ^{2} + 1 ) - 2 x ( x ^{6} + 3 x ^{2} + 50 )}{( x ^{2} + 1 ) ^{2}}

Expand

(6 x^{5} + 6 x) (x^{2} + 1) - 2 x (x^{6} + 3 x^{2} + 50) : 4 x^{7} + 6 x^{5} - 94 x

= \frac{4 x ^{7} + 6 x ^{5} - 94 x}{( x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (cot (6 x))

f (x) = 7 x + 11, (2, 5)

y^{^{'}} = t y - 2 t - 2

\frac{\partial}{\partial x} (\frac{x}{2 y})

What is the derivative of (x^6+3x^2+50)/(x^2+1) ?
The derivative of (x^6+3x^2+50)/(x^2+1) is (4x^7+6x^5-94x)/((x^2+1)^2)
What is the first derivative of (x^6+3x^2+50)/(x^2+1) ?
The first derivative of (x^6+3x^2+50)/(x^2+1) is (4x^7+6x^5-94x)/((x^2+1)^2)