What is the derivative of (x^2-6x+7/(x^2+9)) ?

The derivative of (x^2-6x+7/(x^2+9)) is (6x^2+4x-54)/((x^2+9)^2)

What is the first derivative of (x^2-6x+7/(x^2+9)) ?

The first derivative of (x^2-6x+7/(x^2+9)) is (6x^2+4x-54)/((x^2+9)^2)

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\frac{d}{d x} (\frac{x ^{2} - 6 x + 7}{x ^{2} + 9})

\frac{6 x ^{2} + 4 x - 54}{( x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 6 x + 7}{x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 6 x + 7 ) ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) ( x ^{2} - 6 x + 7 )}{( x ^{2} + 9 ) ^{2}}

\frac{d}{d x} (x^{2} - 6 x + 7) = 2 x - 6

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

= \frac{( 2 x - 6 ) ( x ^{2} + 9 ) - 2 x ( x ^{2} - 6 x + 7 )}{( x ^{2} + 9 ) ^{2}}

Expand

(2 x - 6) (x^{2} + 9) - 2 x (x^{2} - 6 x + 7) : 6 x^{2} + 4 x - 54

= \frac{6 x ^{2} + 4 x - 54}{( x ^{2} + 9 ) ^{2}}

\frac{d}{d x} (\frac{x ^{3}}{1 - x})

f (x) = x^{2} + 2, - 3, 1

\frac{d y}{d x}, y = e^{9 x^{5}}

arccsc (x)

\int \frac{x ^{3} + 2 x - 6}{x ^{3}} d x

What is the derivative of (x^2-6x+7/(x^2+9)) ?
The derivative of (x^2-6x+7/(x^2+9)) is (6x^2+4x-54)/((x^2+9)^2)
What is the first derivative of (x^2-6x+7/(x^2+9)) ?
The first derivative of (x^2-6x+7/(x^2+9)) is (6x^2+4x-54)/((x^2+9)^2)