What is the derivative of (70x/((3x^2+8)^2)) ?

The derivative of (70x/((3x^2+8)^2)) is (70(8-9x^2))/((3x^2+8)^3)

What is the first derivative of (70x/((3x^2+8)^2)) ?

The first derivative of (70x/((3x^2+8)^2)) is (70(8-9x^2))/((3x^2+8)^3)

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\frac{d}{d x} (\frac{70 x}{( 3 x ^{2} + 8 ) ^{2}})

\frac{70 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{70 x}{( 3 x ^{2} + 8 ) ^{2}})

Take the constant out:

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

= 70 \frac{d}{d x} (\frac{x}{( 3 x ^{2} + 8 ) ^{2}})

Apply the Quotient Rule:

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

= 70 \cdot \frac{\frac{d x}{d x} ( 3 x ^{2} + 8 ) ^{2} - \frac{d}{d x} ( ( 3 x ^{2} + 8 ) ^{2} ) x}{( ( 3 x ^{2} + 8 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((3 x^{2} + 8)^{2}) = 12 x (3 x^{2} + 8)

= 70 \cdot \frac{1 \cdot ( 3 x ^{2} + 8 ) ^{2} - 12 x ( 3 x ^{2} + 8 ) x}{( ( 3 x ^{2} + 8 ) ^{2} ) ^{2}}

Simplify

70 \cdot \frac{1 \cdot ( 3 x ^{2} + 8 ) ^{2} - 12 x ( 3 x ^{2} + 8 ) x}{( ( 3 x ^{2} + 8 ) ^{2} ) ^{2}} : \frac{70 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

= \frac{70 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

x \to \infty lim (\frac{x ^{2}}{e ^{4 x}})

3 arctan (x + 1 + x^{2})

\int \frac{cot ( x )}{sin ^{2} ( x )} d x

n = 0 \sum \infty x (1 - x)^{n - 1}

\int 1 - 4 x^{2} d x

What is the derivative of (70x/((3x^2+8)^2)) ?
The derivative of (70x/((3x^2+8)^2)) is (70(8-9x^2))/((3x^2+8)^3)
What is the first derivative of (70x/((3x^2+8)^2)) ?
The first derivative of (70x/((3x^2+8)^2)) is (70(8-9x^2))/((3x^2+8)^3)