What is the derivative of y=(7x^2+5)/(x^2+9) ?

The derivative of y=(7x^2+5)/(x^2+9) is (116x)/((x^2+9)^2)

What is the first derivative of y=(7x^2+5)/(x^2+9) ?

The first derivative of y=(7x^2+5)/(x^2+9) is (116x)/((x^2+9)^2)

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derivative of

y = \frac{7 x ^{2} + 5}{x ^{2} + 9}

\frac{116 x}{( x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x ^{2} + 5}{x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 x ^{2} + 5 ) ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) ( 7 x ^{2} + 5 )}{( x ^{2} + 9 ) ^{2}}

\frac{d}{d x} (7 x^{2} + 5) = 14 x

\frac{d}{d x} (x^{2} + 9) = 2 x

= \frac{14 x ( x ^{2} + 9 ) - 2 x ( 7 x ^{2} + 5 )}{( x ^{2} + 9 ) ^{2}}

Expand

14 x (x^{2} + 9) - 2 x (7 x^{2} + 5) : 116 x

= \frac{116 x}{( x ^{2} + 9 ) ^{2}}

f (x) = x e^{x}

\frac{d x}{d t} = 4000 - \frac{x}{50 + t}

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

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{n ( n ^{2} + 1 ) ^{\frac{1}{2}}}

What is the derivative of y=(7x^2+5)/(x^2+9) ?
The derivative of y=(7x^2+5)/(x^2+9) is (116x)/((x^2+9)^2)
What is the first derivative of y=(7x^2+5)/(x^2+9) ?
The first derivative of y=(7x^2+5)/(x^2+9) is (116x)/((x^2+9)^2)