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

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

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

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

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derivative of

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

\frac{4 x ^{2} + 3}{x ^{2}}

Solution steps

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

\frac{d}{d x} (4 x^{5} + 4 x^{4} - 3 x^{3}) = 20 x^{4} + 16 x^{3} - 9 x^{2}

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

= \frac{( 20 x ^{4} + 16 x ^{3} - 9 x ^{2} ) x ^{4} - 4 x ^{3} ( 4 x ^{5} + 4 x ^{4} - 3 x ^{3} )}{( x ^{4} ) ^{2}}

Simplify

\frac{( 20 x ^{4} + 16 x ^{3} - 9 x ^{2} ) x ^{4} - 4 x ^{3} ( 4 x ^{5} + 4 x ^{4} - 3 x ^{3} )}{( x ^{4} ) ^{2}} : \frac{4 x ^{2} + 3}{x ^{2}}

= \frac{4 x ^{2} + 3}{x ^{2}}

y = 4 + x - 9

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

f (x) = \frac{6}{x}

\int 3 t d t

e^{- 2 t} \cdot (t^{2} + 4 t + 5)

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