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

The derivative of ((x+1^2)/(x+3)) is (x^2+6x+5)/((x+3)^2)

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

The first derivative of ((x+1^2)/(x+3)) is (x^2+6x+5)/((x+3)^2)

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

\frac{x ^{2} + 6 x + 5}{( x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( x + 1 ) ( x + 3 ) - 1 \cdot ( x + 1 ) ^{2}}{( x + 3 ) ^{2}} : \frac{x ^{2} + 6 x + 5}{( x + 3 ) ^{2}}

= \frac{x ^{2} + 6 x + 5}{( x + 3 ) ^{2}}

\frac{d}{d x} (e^{\frac{1}{3} x})

e^{- x} - e^{- x} x

\frac{d}{d x} (e^{x - 4})

\frac{d y}{d x} = (1 + y^{2}) tan (x), y (0) = 1

x \to 1 lim (2 x)

What is the derivative of ((x+1^2)/(x+3)) ?
The derivative of ((x+1^2)/(x+3)) is (x^2+6x+5)/((x+3)^2)
What is the first derivative of ((x+1^2)/(x+3)) ?
The first derivative of ((x+1^2)/(x+3)) is (x^2+6x+5)/((x+3)^2)