What is the derivative of (4x^2/((7-5x)^3)) ?

The derivative of (4x^2/((7-5x)^3)) is (4x(5x+14))/((7-5x)^4)

What is the first derivative of (4x^2/((7-5x)^3)) ?

The first derivative of (4x^2/((7-5x)^3)) is (4x(5x+14))/((7-5x)^4)

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\frac{d}{d x} (\frac{4 x ^{2}}{( 7 - 5 x ) ^{3}})

\frac{4 x ( 5 x + 14 )}{( 7 - 5 x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2}}{( 7 - 5 x ) ^{3}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x ^{2}}{( 7 - 5 x ) ^{3}})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 7 - 5 x ) ^{3} - \frac{d}{d x} ( ( 7 - 5 x ) ^{3} ) x ^{2}}{( ( 7 - 5 x ) ^{3} ) ^{2}}

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

\frac{d}{d x} ((7 - 5 x)^{3}) = - 15 (7 - 5 x)^{2}

= 4 \cdot \frac{2 x ( 7 - 5 x ) ^{3} - ( - 15 ( 7 - 5 x ) ^{2} ) x ^{2}}{( ( 7 - 5 x ) ^{3} ) ^{2}}

Simplify

4 \cdot \frac{2 x ( 7 - 5 x ) ^{3} - ( - 15 ( 7 - 5 x ) ^{2} ) x ^{2}}{( ( 7 - 5 x ) ^{3} ) ^{2}} : \frac{4 x ( 5 x + 14 )}{( 7 - 5 x ) ^{4}}

= \frac{4 x ( 5 x + 14 )}{( 7 - 5 x ) ^{4}}

What is the derivative of (4x^2/((7-5x)^3)) ?
The derivative of (4x^2/((7-5x)^3)) is (4x(5x+14))/((7-5x)^4)
What is the first derivative of (4x^2/((7-5x)^3)) ?
The first derivative of (4x^2/((7-5x)^3)) is (4x(5x+14))/((7-5x)^4)