What is the derivative of (2x^5-3x^4-7x^3/(x^4)) ?

The derivative of (2x^5-3x^4-7x^3/(x^4)) is (2x^2+7)/(x^2)

What is the first derivative of (2x^5-3x^4-7x^3/(x^4)) ?

The first derivative of (2x^5-3x^4-7x^3/(x^4)) is (2x^2+7)/(x^2)

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\frac{d}{d x} (\frac{2 x ^{5} - 3 x ^{4} - 7 x ^{3}}{x ^{4}})

\frac{2 x ^{2} + 7}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{5} - 3 x ^{4} - 7 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} ( 2 x ^{5} - 3 x ^{4} - 7 x ^{3} ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 2 x ^{5} - 3 x ^{4} - 7 x ^{3} )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (2 x^{5} - 3 x^{4} - 7 x^{3}) = 10 x^{4} - 12 x^{3} - 21 x^{2}

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

= \frac{( 10 x ^{4} - 12 x ^{3} - 21 x ^{2} ) x ^{4} - 4 x ^{3} ( 2 x ^{5} - 3 x ^{4} - 7 x ^{3} )}{( x ^{4} ) ^{2}}

Simplify

\frac{( 10 x ^{4} - 12 x ^{3} - 21 x ^{2} ) x ^{4} - 4 x ^{3} ( 2 x ^{5} - 3 x ^{4} - 7 x ^{3} )}{( x ^{4} ) ^{2}} : \frac{2 x ^{2} + 7}{x ^{2}}

= \frac{2 x ^{2} + 7}{x ^{2}}

\int sin (3 θ) cos (5 θ) d θ

2 (t - 2)^{2} + 7 (t - 2) + 9

\frac{d}{d x} (sin (2 x^{3} + x^{2} + 1))

x \to 0 lim (\frac{a x - a ln ( x + 1 )}{x ln ( x + 1 )})

\frac{d}{d t} (1 - cos (t) - sin (t))

What is the derivative of (2x^5-3x^4-7x^3/(x^4)) ?
The derivative of (2x^5-3x^4-7x^3/(x^4)) is (2x^2+7)/(x^2)
What is the first derivative of (2x^5-3x^4-7x^3/(x^4)) ?
The first derivative of (2x^5-3x^4-7x^3/(x^4)) is (2x^2+7)/(x^2)