What is the derivative of (4x/(5x^2+3)) ?

The derivative of (4x/(5x^2+3)) is (4(-5x^2+3))/((5x^2+3)^2)

What is the first derivative of (4x/(5x^2+3)) ?

The first derivative of (4x/(5x^2+3)) is (4(-5x^2+3))/((5x^2+3)^2)

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\frac{d}{d x} (\frac{4 x}{5 x ^{2} + 3})

\frac{4 ( - 5 x ^{2} + 3 )}{( 5 x ^{2} + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x}{5 x ^{2} + 3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{x}{5 x ^{2} + 3})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} ( 5 x ^{2} + 3 ) - \frac{d}{d x} ( 5 x ^{2} + 3 ) x}{( 5 x ^{2} + 3 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= 4 \cdot \frac{1 \cdot ( 5 x ^{2} + 3 ) - 10 xx}{( 5 x ^{2} + 3 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( 5 x ^{2} + 3 ) - 10 xx}{( 5 x ^{2} + 3 ) ^{2}} : \frac{4 ( - 5 x ^{2} + 3 )}{( 5 x ^{2} + 3 ) ^{2}}

= \frac{4 ( - 5 x ^{2} + 3 )}{( 5 x ^{2} + 3 ) ^{2}}

\int \frac{8}{36 x ^{2} + 4} d x

\frac{d}{d x} (e^{- x} cos (\frac{x}{2}))

\frac{\partial}{\partial v} (3 u sin (v))

\frac{d y}{d x} + y^{3} x + 6 y = 0

x \to 0 lim (cos (2 x))

What is the derivative of (4x/(5x^2+3)) ?
The derivative of (4x/(5x^2+3)) is (4(-5x^2+3))/((5x^2+3)^2)
What is the first derivative of (4x/(5x^2+3)) ?
The first derivative of (4x/(5x^2+3)) is (4(-5x^2+3))/((5x^2+3)^2)