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

The derivative of y=(5x^2+3)/(x^2+1) is (4x)/((x^2+1)^2)

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

The first derivative of y=(5x^2+3)/(x^2+1) is (4x)/((x^2+1)^2)

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derivative of

y = \frac{5 x ^{2} + 3}{x ^{2} + 1}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x^{2} + 3) = 10 x

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

= \frac{10 x ( x ^{2} + 1 ) - 2 x ( 5 x ^{2} + 3 )}{( x ^{2} + 1 ) ^{2}}

Expand

10 x (x^{2} + 1) - 2 x (5 x^{2} + 3) : 4 x

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

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

x \to 7 lim (2 x^{- 1})

f (x) = \frac{x ^{12}}{x ^{2}}

\frac{8 x}{x ^{2} + 1}

\frac{d}{d x} (2 (x^{2} + y^{2})^{2})

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