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

The derivative of (4x^2-3/(x+4)) is (4x^2+32x+3)/((x+4)^2)

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

The first derivative of (4x^2-3/(x+4)) is (4x^2+32x+3)/((x+4)^2)

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

\frac{4 x ^{2} + 32 x + 3}{( x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{2} - 3) = 8 x

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

= \frac{8 x ( x + 4 ) - 1 \cdot ( 4 x ^{2} - 3 )}{( x + 4 ) ^{2}}

Simplify

\frac{8 x ( x + 4 ) - 1 \cdot ( 4 x ^{2} - 3 )}{( x + 4 ) ^{2}} : \frac{4 x ^{2} + 32 x + 3}{( x + 4 ) ^{2}}

= \frac{4 x ^{2} + 32 x + 3}{( x + 4 ) ^{2}}

\frac{d}{d x} ((2 x + 8)^{2})

x \to 0 lim (\frac{sin ( 5 ) ( x )}{x})

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

arccos (1) (4 x^{2})

\int_{0}^{N} e^{- s t} cos (2 t) d t

What is the derivative of (4x^2-3/(x+4)) ?
The derivative of (4x^2-3/(x+4)) is (4x^2+32x+3)/((x+4)^2)
What is the first derivative of (4x^2-3/(x+4)) ?
The first derivative of (4x^2-3/(x+4)) is (4x^2+32x+3)/((x+4)^2)