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

The derivative of ((3x^2))/((5-3x)^4) is (6x(3x+5))/((5-3x)^5)

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

The first derivative of ((3x^2))/((5-3x)^4) is (6x(3x+5))/((5-3x)^5)

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derivative of

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

\frac{6 x ( 3 x + 5 )}{( 5 - 3 x ) ^{5}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

3 \cdot \frac{2 x ( 5 - 3 x ) ^{4} - ( - 12 ( 5 - 3 x ) ^{3} ) x ^{2}}{( ( 5 - 3 x ) ^{4} ) ^{2}} : \frac{6 x ( 3 x + 5 )}{( 5 - 3 x ) ^{5}}

= \frac{6 x ( 3 x + 5 )}{( 5 - 3 x ) ^{5}}

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

\int (8 + x) d x

\frac{d y}{d x}, x^{2} y + x y^{2} = 6

\int \frac{1}{3 - 4 x} d x

\frac{d}{d x} (\frac{x}{9.8})

What is the derivative of ((3x^2))/((5-3x)^4) ?
The derivative of ((3x^2))/((5-3x)^4) is (6x(3x+5))/((5-3x)^5)
What is the first derivative of ((3x^2))/((5-3x)^4) ?
The first derivative of ((3x^2))/((5-3x)^4) is (6x(3x+5))/((5-3x)^5)