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

The derivative of (4x^5-5x^4+6x-2/(x^4)) is (2(2x^5-9x+4))/(x^5)

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

The first derivative of (4x^5-5x^4+6x-2/(x^4)) is (2(2x^5-9x+4))/(x^5)

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\frac{d}{d x} (\frac{4 x ^{5} - 5 x ^{4} + 6 x - 2}{x ^{4}})

\frac{2 ( 2 x ^{5} - 9 x + 4 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{5} - 5 x ^{4} + 6 x - 2}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{5} - 5 x ^{4} + 6 x - 2 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 4 x ^{5} - 5 x ^{4} + 6 x - 2 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (4 x^{5} - 5 x^{4} + 6 x - 2) = 20 x^{4} - 20 x^{3} + 6

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

= \frac{( 20 x ^{4} - 20 x ^{3} + 6 ) x ^{4} - 4 x ^{3} ( 4 x ^{5} - 5 x ^{4} + 6 x - 2 )}{( x ^{4} ) ^{2}}

Simplify

\frac{( 20 x ^{4} - 20 x ^{3} + 6 ) x ^{4} - 4 x ^{3} ( 4 x ^{5} - 5 x ^{4} + 6 x - 2 )}{( x ^{4} ) ^{2}} : \frac{2 ( 2 x ^{5} - 9 x + 4 )}{x ^{5}}

= \frac{2 ( 2 x ^{5} - 9 x + 4 )}{x ^{5}}

y^{^{'}} + 3 y + 5 = 0

\frac{d}{d x} (3 x^{2} + 12 x + 6)

Y = (x^{\frac{1}{2}}), Y = 6 - x, Y = 0

\int e^{x - 3} d x

e^{x}, e^{- 3 x}, x = ln (4)

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