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

The derivative of ((x^2+1)/((x+4))) is (x^2+8x-1)/((x+4)^2)

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

The first derivative of ((x^2+1)/((x+4))) is (x^2+8x-1)/((x+4)^2)

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

\frac{x ^{2} + 8 x - 1}{( x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 4) = 1

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

Simplify

\frac{2 x ( x + 4 ) - 1 \cdot ( x ^{2} + 1 )}{( x + 4 ) ^{2}} : \frac{x ^{2} + 8 x - 1}{( x + 4 ) ^{2}}

= \frac{x ^{2} + 8 x - 1}{( x + 4 ) ^{2}}

y = (5 x + 1)^{3} (x - 4)

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

sin (8 x)

\int_{0}^{5} \frac{1}{x ^{\frac{13}{14}}} d x

y^{^{''}} + 2 y^{^{'}} - 2 y = 0

What is the derivative of ((x^2+1)/((x+4))) ?
The derivative of ((x^2+1)/((x+4))) is (x^2+8x-1)/((x+4)^2)
What is the first derivative of ((x^2+1)/((x+4))) ?
The first derivative of ((x^2+1)/((x+4))) is (x^2+8x-1)/((x+4)^2)