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

The derivative of (2x^9-5x+sqrt(x))/(x^4) is (20x^9+30x-7sqrt(x))/(2x^5)

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

The first derivative of (2x^9-5x+sqrt(x))/(x^4) is (20x^9+30x-7sqrt(x))/(2x^5)

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derivative of

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

\frac{20 x ^{9} + 30 x - 7 x}{2 x ^{5}}

Solution steps

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

\frac{d}{d x} (2 x^{9} - 5 x + x) = 18 x^{8} - 5 + \frac{1}{2 x}

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

= \frac{( 18 x ^{8} - 5 + \frac{1}{2 x} ) x ^{4} - 4 x ^{3} ( 2 x ^{9} - 5 x + x )}{( x ^{4} ) ^{2}}

Simplify

\frac{( 18 x ^{8} - 5 + \frac{1}{2 x} ) x ^{4} - 4 x ^{3} ( 2 x ^{9} - 5 x + x )}{( x ^{4} ) ^{2}} : \frac{20 x ^{9} + 30 x - 7 x}{2 x ^{5}}

= \frac{20 x ^{9} + 30 x - 7 x}{2 x ^{5}}

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

(e^{2 x} + 4) (\frac{d y}{d x}) = y

\frac{d}{d x} (2 x - ln (x))

y^{^{'}} = - k y

What is the derivative of (2x^9-5x+sqrt(x))/(x^4) ?
The derivative of (2x^9-5x+sqrt(x))/(x^4) is (20x^9+30x-7sqrt(x))/(2x^5)
What is the first derivative of (2x^9-5x+sqrt(x))/(x^4) ?
The first derivative of (2x^9-5x+sqrt(x))/(x^4) is (20x^9+30x-7sqrt(x))/(2x^5)