What is the derivative of (x^2+4x+5x^3/(x+1)) ?

The derivative of (x^2+4x+5x^3/(x+1)) is (10x^3+16x^2+2x+4)/((x+1)^2)

What is the first derivative of (x^2+4x+5x^3/(x+1)) ?

The first derivative of (x^2+4x+5x^3/(x+1)) is (10x^3+16x^2+2x+4)/((x+1)^2)

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\frac{d}{d x} (\frac{x ^{2} + 4 x + 5 x ^{3}}{x + 1})

\frac{10 x ^{3} + 16 x ^{2} + 2 x + 4}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 4 x + 5 x ^{3}}{x + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 4 x + 5 x ^{3} ) ( x + 1 ) - \frac{d}{d x} ( x + 1 ) ( x ^{2} + 4 x + 5 x ^{3} )}{( x + 1 ) ^{2}}

\frac{d}{d x} (x^{2} + 4 x + 5 x^{3}) = 2 x + 4 + 15 x^{2}

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

= \frac{( 2 x + 4 + 15 x ^{2} ) ( x + 1 ) - 1 \cdot ( x ^{2} + 4 x + 5 x ^{3} )}{( x + 1 ) ^{2}}

Simplify

\frac{( 2 x + 4 + 15 x ^{2} ) ( x + 1 ) - 1 \cdot ( x ^{2} + 4 x + 5 x ^{3} )}{( x + 1 ) ^{2}} : \frac{10 x ^{3} + 16 x ^{2} + 2 x + 4}{( x + 1 ) ^{2}}

= \frac{10 x ^{3} + 16 x ^{2} + 2 x + 4}{( x + 1 ) ^{2}}

\int_{1}^{2} 2^{- x} d x

\int_{0}^{1} \frac{25}{4 y - 1} d y

x \to 0 + lim (x ln (x + x^{2}))

\frac{d P}{d x} = P - P^{2}

\frac{d}{d x} (3 x - 6)

What is the derivative of (x^2+4x+5x^3/(x+1)) ?
The derivative of (x^2+4x+5x^3/(x+1)) is (10x^3+16x^2+2x+4)/((x+1)^2)
What is the first derivative of (x^2+4x+5x^3/(x+1)) ?
The first derivative of (x^2+4x+5x^3/(x+1)) is (10x^3+16x^2+2x+4)/((x+1)^2)