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

The derivative of f(x)=((4x)^3)/((3-5x)^5) is (64x^2(10x+9))/((3-5x)^6)

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

The first derivative of f(x)=((4x)^3)/((3-5x)^5) is (64x^2(10x+9))/((3-5x)^6)

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derivative of

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

\frac{64 x ^{2} ( 10 x + 9 )}{( 3 - 5 x ) ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((4 x)^{3}) = 192 x^{2}

\frac{d}{d x} ((3 - 5 x)^{5}) = - 25 (3 - 5 x)^{4}

= \frac{192 x ^{2} ( 3 - 5 x ) ^{5} - ( - 25 ( 3 - 5 x ) ^{4} ) ( 4 x ) ^{3}}{( ( 3 - 5 x ) ^{5} ) ^{2}}

Simplify

\frac{192 x ^{2} ( 3 - 5 x ) ^{5} - ( - 25 ( 3 - 5 x ) ^{4} ) ( 4 x ) ^{3}}{( ( 3 - 5 x ) ^{5} ) ^{2}} : \frac{64 x ^{2} ( 10 x + 9 )}{( 3 - 5 x ) ^{6}}

= \frac{64 x ^{2} ( 10 x + 9 )}{( 3 - 5 x ) ^{6}}

\int 4 x ln (4 x) d x

ln (e^{x} x)

\frac{1}{1 - x}, (\frac{π}{4})

\int \frac{( 2 x + 1 )}{( x + 2 ) ^{4} ( x - 1 ) ^{4}} d x

\frac{d y}{d x} = 3 x^{2} e^{- y}

What is the derivative of f(x)=((4x)^3)/((3-5x)^5) ?
The derivative of f(x)=((4x)^3)/((3-5x)^5) is (64x^2(10x+9))/((3-5x)^6)
What is the first derivative of f(x)=((4x)^3)/((3-5x)^5) ?
The first derivative of f(x)=((4x)^3)/((3-5x)^5) is (64x^2(10x+9))/((3-5x)^6)