What is the derivative of y=((2x^2+7))/(x^2+3) ?

The derivative of y=((2x^2+7))/(x^2+3) is -(2x)/((x^2+3)^2)

What is the first derivative of y=((2x^2+7))/(x^2+3) ?

The first derivative of y=((2x^2+7))/(x^2+3) is -(2x)/((x^2+3)^2)

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derivative of

y = \frac{( 2 x ^{2} + 7 )}{x ^{2} + 3}

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

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} + 7}{x ^{2} + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} + 7 ) ( x ^{2} + 3 ) - \frac{d}{d x} ( x ^{2} + 3 ) ( 2 x ^{2} + 7 )}{( x ^{2} + 3 ) ^{2}}

\frac{d}{d x} (2 x^{2} + 7) = 4 x

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

= \frac{4 x ( x ^{2} + 3 ) - 2 x ( 2 x ^{2} + 7 )}{( x ^{2} + 3 ) ^{2}}

Simplify

\frac{4 x ( x ^{2} + 3 ) - 2 x ( 2 x ^{2} + 7 )}{( x ^{2} + 3 ) ^{2}} : - \frac{2 x}{( x ^{2} + 3 ) ^{2}}

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

x \to 3 π + lim (csc (x))

f (x) = - \frac{5}{x ^{2}}

4 x y (\frac{d y}{d x}) = 1

\int \frac{5}{4 x ^{2} - 49} d x

\int_{6}^{8} \frac{26}{( x - 6 ) ^{3}} d x

What is the derivative of y=((2x^2+7))/(x^2+3) ?
The derivative of y=((2x^2+7))/(x^2+3) is -(2x)/((x^2+3)^2)
What is the first derivative of y=((2x^2+7))/(x^2+3) ?
The first derivative of y=((2x^2+7))/(x^2+3) is -(2x)/((x^2+3)^2)