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

The derivative of (x^2+x+m^2/(x+1)) is (x^2+2x-m^2+1)/((x+1)^2)

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

The first derivative of (x^2+x+m^2/(x+1)) is (x^2+2x-m^2+1)/((x+1)^2)

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

\frac{x ^{2} + 2 x - m ^{2} + 1}{( x + 1 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{( 2 x + 1 ) ( x + 1 ) - 1 \cdot ( x ^{2} + x + m ^{2} )}{( x + 1 ) ^{2}} : \frac{x ^{2} + 2 x - m ^{2} + 1}{( x + 1 ) ^{2}}

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

6 cos (\frac{x}{2})

(5^{x})^{7}

x^{2} + a^{2}

x - 3 x^{\frac{1}{3}}

\frac{d}{d p} (p^{4} + a^{6.2} - c^{6.3})

What is the derivative of (x^2+x+m^2/(x+1)) ?
The derivative of (x^2+x+m^2/(x+1)) is (x^2+2x-m^2+1)/((x+1)^2)
What is the first derivative of (x^2+x+m^2/(x+1)) ?
The first derivative of (x^2+x+m^2/(x+1)) is (x^2+2x-m^2+1)/((x+1)^2)