What is the derivative of (x+7/(x^3+x-6)) ?

The derivative of (x+7/(x^3+x-6)) is (-2x^3-21x^2-13)/((x^3+x-6)^2)

What is the first derivative of (x+7/(x^3+x-6)) ?

The first derivative of (x+7/(x^3+x-6)) is (-2x^3-21x^2-13)/((x^3+x-6)^2)

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\frac{d}{d x} (\frac{x + 7}{x ^{3} + x - 6})

\frac{- 2 x ^{3} - 21 x ^{2} - 13}{( x ^{3} + x - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 7}{x ^{3} + x - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 7 ) ( x ^{3} + x - 6 ) - \frac{d}{d x} ( x ^{3} + x - 6 ) ( x + 7 )}{( x ^{3} + x - 6 ) ^{2}}

\frac{d}{d x} (x + 7) = 1

\frac{d}{d x} (x^{3} + x - 6) = 3 x^{2} + 1

= \frac{1 \cdot ( x ^{3} + x - 6 ) - ( 3 x ^{2} + 1 ) ( x + 7 )}{( x ^{3} + x - 6 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{3} + x - 6 ) - ( 3 x ^{2} + 1 ) ( x + 7 )}{( x ^{3} + x - 6 ) ^{2}} : \frac{- 2 x ^{3} - 21 x ^{2} - 13}{( x ^{3} + x - 6 ) ^{2}}

= \frac{- 2 x ^{3} - 21 x ^{2} - 13}{( x ^{3} + x - 6 ) ^{2}}

x \to 1 lim (- x^{2} + 1)

x \cdot \frac{d y}{d x} + 7 y = \frac{1}{x}

\int e^{5 x} sin (5 x) d x

y = cos (x), x = \frac{π}{4}, x = \frac{π}{3}

\frac{d y}{d x} + y = 0

What is the derivative of (x+7/(x^3+x-6)) ?
The derivative of (x+7/(x^3+x-6)) is (-2x^3-21x^2-13)/((x^3+x-6)^2)
What is the first derivative of (x+7/(x^3+x-6)) ?
The first derivative of (x+7/(x^3+x-6)) is (-2x^3-21x^2-13)/((x^3+x-6)^2)