What is the derivative of (2x^2+1)/(x^2+8) ?

The derivative of (2x^2+1)/(x^2+8) is (30x)/((x^2+8)^2)

What is the first derivative of (2x^2+1)/(x^2+8) ?

The first derivative of (2x^2+1)/(x^2+8) is (30x)/((x^2+8)^2)

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derivative of

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

\frac{30 x}{( x ^{2} + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} + 1}{x ^{2} + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} + 1 ) ( x ^{2} + 8 ) - \frac{d}{d x} ( x ^{2} + 8 ) ( 2 x ^{2} + 1 )}{( x ^{2} + 8 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 8) = 2 x

= \frac{4 x ( x ^{2} + 8 ) - 2 x ( 2 x ^{2} + 1 )}{( x ^{2} + 8 ) ^{2}}

Expand

4 x (x^{2} + 8) - 2 x (2 x^{2} + 1) : 30 x

= \frac{30 x}{( x ^{2} + 8 ) ^{2}}

\int_{0}^{1} ln (x^{2} + 1) d x

\int \frac{1}{x ^{2} + x + 1} d x

- \frac{3 ( z ^{2} + 1 )}{z ^{2}}

y^{2} = 6 - x, 3 y = x + 12

\int_{π}^{2 π} 9 x sin (x) d x

What is the derivative of (2x^2+1)/(x^2+8) ?
The derivative of (2x^2+1)/(x^2+8) is (30x)/((x^2+8)^2)
What is the first derivative of (2x^2+1)/(x^2+8) ?
The first derivative of (2x^2+1)/(x^2+8) is (30x)/((x^2+8)^2)