What is the derivative of x/(a^2x^2+bx+49) ?

The derivative of x/(a^2x^2+bx+49) is (-a^2x^2+49)/((a^2x^2+bx+49)^2)

What is the first derivative of x/(a^2x^2+bx+49) ?

The first derivative of x/(a^2x^2+bx+49) is (-a^2x^2+49)/((a^2x^2+bx+49)^2)

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\frac{d}{d x} (\frac{x}{a ^{2} x ^{2} + b x + 49})

\frac{- a ^{2} x ^{2} + 49}{( a ^{2} x ^{2} + b x + 49 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{a ^{2} x ^{2} + b x + 49})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( a ^{2} x ^{2} + b x + 49 ) - \frac{d}{d x} ( a ^{2} x ^{2} + b x + 49 ) x}{( a ^{2} x ^{2} + b x + 49 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (a^{2} x^{2} + b x + 49) = 2 a^{2} x + b

= \frac{1 \cdot ( a ^{2} x ^{2} + b x + 49 ) - ( 2 a ^{2} x + b ) x}{( a ^{2} x ^{2} + b x + 49 ) ^{2}}

Simplify

\frac{1 \cdot ( a ^{2} x ^{2} + b x + 49 ) - ( 2 a ^{2} x + b ) x}{( a ^{2} x ^{2} + b x + 49 ) ^{2}} : \frac{- a ^{2} x ^{2} + 49}{( a ^{2} x ^{2} + b x + 49 ) ^{2}}

= \frac{- a ^{2} x ^{2} + 49}{( a ^{2} x ^{2} + b x + 49 ) ^{2}}

\int \frac{x ^{2} + 5 x - 8}{x} d x

x \to \infty lim (2 x + 8)

17 x

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

x \to 2 lim (a^{2} x + 2 a)

What is the derivative of x/(a^2x^2+bx+49) ?
The derivative of x/(a^2x^2+bx+49) is (-a^2x^2+49)/((a^2x^2+bx+49)^2)
What is the first derivative of x/(a^2x^2+bx+49) ?
The first derivative of x/(a^2x^2+bx+49) is (-a^2x^2+49)/((a^2x^2+bx+49)^2)