What is the derivative of (x+3/(x^3+x-5)) ?

The derivative of (x+3/(x^3+x-5)) is (-2x^3-9x^2-8)/((x^3+x-5)^2)

What is the first derivative of (x+3/(x^3+x-5)) ?

The first derivative of (x+3/(x^3+x-5)) is (-2x^3-9x^2-8)/((x^3+x-5)^2)

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\frac{d}{d x} (\frac{x + 3}{x ^{3} + x - 5})

\frac{- 2 x ^{3} - 9 x ^{2} - 8}{( x ^{3} + x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 3}{x ^{3} + x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 3 ) ( x ^{3} + x - 5 ) - \frac{d}{d x} ( x ^{3} + x - 5 ) ( x + 3 )}{( x ^{3} + x - 5 ) ^{2}}

\frac{d}{d x} (x + 3) = 1

\frac{d}{d x} (x^{3} + x - 5) = 3 x^{2} + 1

= \frac{1 \cdot ( x ^{3} + x - 5 ) - ( 3 x ^{2} + 1 ) ( x + 3 )}{( x ^{3} + x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{3} + x - 5 ) - ( 3 x ^{2} + 1 ) ( x + 3 )}{( x ^{3} + x - 5 ) ^{2}} : \frac{- 2 x ^{3} - 9 x ^{2} - 8}{( x ^{3} + x - 5 ) ^{2}}

= \frac{- 2 x ^{3} - 9 x ^{2} - 8}{( x ^{3} + x - 5 ) ^{2}}

\int_{0}^{2 π} sin^{2} (3 x) d x

\int \frac{x}{5 - x} d x

\int \frac{5}{36 + ( x - 1 ) ^{2}} d x

\int \frac{14}{x ( x ^{2} + 4 ) ^{2}} d x

(ln (t^{2} + 1))^{^{'}}

What is the derivative of (x+3/(x^3+x-5)) ?
The derivative of (x+3/(x^3+x-5)) is (-2x^3-9x^2-8)/((x^3+x-5)^2)
What is the first derivative of (x+3/(x^3+x-5)) ?
The first derivative of (x+3/(x^3+x-5)) is (-2x^3-9x^2-8)/((x^3+x-5)^2)