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

The derivative of (5x^3)/((5-3x)^4) is (15x^2(x+5))/((5-3x)^5)

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

The first derivative of (5x^3)/((5-3x)^4) is (15x^2(x+5))/((5-3x)^5)

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derivative of

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

\frac{15 x ^{2} ( x + 5 )}{( 5 - 3 x ) ^{5}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((5 - 3 x)^{4}) = - 12 (5 - 3 x)^{3}

= 5 \cdot \frac{3 x ^{2} ( 5 - 3 x ) ^{4} - ( - 12 ( 5 - 3 x ) ^{3} ) x ^{3}}{( ( 5 - 3 x ) ^{4} ) ^{2}}

Simplify

5 \cdot \frac{3 x ^{2} ( 5 - 3 x ) ^{4} - ( - 12 ( 5 - 3 x ) ^{3} ) x ^{3}}{( ( 5 - 3 x ) ^{4} ) ^{2}} : \frac{15 x ^{2} ( x + 5 )}{( 5 - 3 x ) ^{5}}

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

f (x) = 5 (x^{3} - x)^{4}

\frac{d}{d x} (\frac{( x - 2 )}{x - 1})

h (x) = (x + 1)^{7} - 7 x - 3

\int e^{x} cos (7 x) d x

2 x, x, 2

What is the derivative of (5x^3)/((5-3x)^4) ?
The derivative of (5x^3)/((5-3x)^4) is (15x^2(x+5))/((5-3x)^5)
What is the first derivative of (5x^3)/((5-3x)^4) ?
The first derivative of (5x^3)/((5-3x)^4) is (15x^2(x+5))/((5-3x)^5)