What is the derivative of 1/(a+bx+cx^2+0.003) ?

The derivative of 1/(a+bx+cx^2+0.003) is -(2cx+b)/((cx^2+bx+a)^2)

What is the first derivative of 1/(a+bx+cx^2+0.003) ?

The first derivative of 1/(a+bx+cx^2+0.003) is -(2cx+b)/((cx^2+bx+a)^2)

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\frac{d}{d x} (\frac{1}{a + b x + c x ^{2}} + 0.003)

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

Solution steps

\frac{d}{d x} (\frac{1}{a + b x + c x ^{2}} + 0.003)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{a + b x + c x ^{2}}) + \frac{d}{d x} (0.003)

\frac{d}{d x} (\frac{1}{a + b x + c x ^{2}}) = - \frac{2 c x + b}{( a + b x + c x ^{2} ) ^{2}}

\frac{d}{d x} (0.003) = 0

= - \frac{2 c x + b}{( a + b x + c x ^{2} ) ^{2}} + 0

Simplify

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

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\frac{d y}{d x} = \frac{x - 1}{y + 2}

x \to 3 lim (x^{2} - 2)

\int \frac{1}{3 8 - x} d x

\int \frac{1}{12 x ^{7}} d x

What is the derivative of 1/(a+bx+cx^2+0.003) ?
The derivative of 1/(a+bx+cx^2+0.003) is -(2cx+b)/((cx^2+bx+a)^2)
What is the first derivative of 1/(a+bx+cx^2+0.003) ?
The first derivative of 1/(a+bx+cx^2+0.003) is -(2cx+b)/((cx^2+bx+a)^2)