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}}

7 x^{2} y^{^{''}} + 15 x y^{^{'}} + y = 0

(x^{3} - 6 x^{2} + 2 x - 2)^{^{'}}

sin (x) + \frac{1}{2} cot (x)

y = \frac{ln ( x )}{1 + ln ( x )}

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

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)