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

The derivative of ((4x-2^4)/((-5x+1)^5)) is (2(4x-2)^3(10x-17))/((-5x+1)^6)

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

The first derivative of ((4x-2^4)/((-5x+1)^5)) is (2(4x-2)^3(10x-17))/((-5x+1)^6)

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

\frac{2 ( 4 x - 2 ) ^{3} ( 10 x - 17 )}{( - 5 x + 1 ) ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((4 x - 2)^{4}) = 16 (4 x - 2)^{3}

\frac{d}{d x} ((- 5 x + 1)^{5}) = - 25 (- 5 x + 1)^{4}

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

Simplify

\frac{16 ( 4 x - 2 ) ^{3} ( - 5 x + 1 ) ^{5} - ( - 25 ( - 5 x + 1 ) ^{4} ) ( 4 x - 2 ) ^{4}}{( ( - 5 x + 1 ) ^{5} ) ^{2}} : \frac{2 ( 4 x - 2 ) ^{3} ( 10 x - 17 )}{( - 5 x + 1 ) ^{6}}

= \frac{2 ( 4 x - 2 ) ^{3} ( 10 x - 17 )}{( - 5 x + 1 ) ^{6}}

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

\frac{d y}{d x}, x = y^{4}

y^{^{'}} - \frac{6}{x} y = x^{9} y^{8}

\int - \frac{1}{csc ( y )} d y

What is the derivative of ((4x-2^4)/((-5x+1)^5)) ?
The derivative of ((4x-2^4)/((-5x+1)^5)) is (2(4x-2)^3(10x-17))/((-5x+1)^6)
What is the first derivative of ((4x-2^4)/((-5x+1)^5)) ?
The first derivative of ((4x-2^4)/((-5x+1)^5)) is (2(4x-2)^3(10x-17))/((-5x+1)^6)