What is the derivative of ((5x+2)^5)/((4x+1)^4) ?

The derivative of ((5x+2)^5)/((4x+1)^4) is ((5x+2)^4(20x-7))/((4x+1)^5)

What is the first derivative of ((5x+2)^5)/((4x+1)^4) ?

The first derivative of ((5x+2)^5)/((4x+1)^4) is ((5x+2)^4(20x-7))/((4x+1)^5)

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derivative of

\frac{( 5 x + 2 ) ^{5}}{( 4 x + 1 ) ^{4}}

\frac{( 5 x + 2 ) ^{4} ( 20 x - 7 )}{( 4 x + 1 ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{( 5 x + 2 ) ^{5}}{( 4 x + 1 ) ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( 5 x + 2 ) ^{5} ) ( 4 x + 1 ) ^{4} - \frac{d}{d x} ( ( 4 x + 1 ) ^{4} ) ( 5 x + 2 ) ^{5}}{( ( 4 x + 1 ) ^{4} ) ^{2}}

\frac{d}{d x} ((5 x + 2)^{5}) = 25 (5 x + 2)^{4}

\frac{d}{d x} ((4 x + 1)^{4}) = 16 (4 x + 1)^{3}

= \frac{25 ( 5 x + 2 ) ^{4} ( 4 x + 1 ) ^{4} - 16 ( 4 x + 1 ) ^{3} ( 5 x + 2 ) ^{5}}{( ( 4 x + 1 ) ^{4} ) ^{2}}

Simplify

\frac{25 ( 5 x + 2 ) ^{4} ( 4 x + 1 ) ^{4} - 16 ( 4 x + 1 ) ^{3} ( 5 x + 2 ) ^{5}}{( ( 4 x + 1 ) ^{4} ) ^{2}} : \frac{( 5 x + 2 ) ^{4} ( 20 x - 7 )}{( 4 x + 1 ) ^{5}}

= \frac{( 5 x + 2 ) ^{4} ( 20 x - 7 )}{( 4 x + 1 ) ^{5}}

y^{^{''}} + 4 y = 5

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

\frac{\partial}{\partial t} (e^{- 9 t} cos (π x))

6 x (x + 3 y) y^{^{'}} = 6 y (x - 3 y)

\frac{d y}{d x} = x^{2} e^{- 4 x} - 4 y

What is the derivative of ((5x+2)^5)/((4x+1)^4) ?
The derivative of ((5x+2)^5)/((4x+1)^4) is ((5x+2)^4(20x-7))/((4x+1)^5)
What is the first derivative of ((5x+2)^5)/((4x+1)^4) ?
The first derivative of ((5x+2)^5)/((4x+1)^4) is ((5x+2)^4(20x-7))/((4x+1)^5)