What is the derivative of 1/5 x^5-1/(2x^4+3x+9) ?

The derivative of 1/5 x^5-1/(2x^4+3x+9) is x^4+2/(x^5)+3

What is the first derivative of 1/5 x^5-1/(2x^4+3x+9) ?

The first derivative of 1/5 x^5-1/(2x^4+3x+9) is x^4+2/(x^5)+3

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

x^{4} + \frac{2}{x ^{5}} + 3

Solution steps

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

Simplify

\frac{1}{5} x^{5} - \frac{1}{2 x ^{4}} + 3 x + 9 : \frac{x ^{5}}{5} - \frac{1}{2 x ^{4}} + 3 x + 9

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (\frac{x ^{5}}{5}) = x^{4}

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

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

\frac{d}{d x} (9) = 0

= x^{4} - (- \frac{2}{x ^{5}}) + 3 + 0

Simplify

= x^{4} + \frac{2}{x ^{5}} + 3

y^{^{''}} + 5 y^{^{'}} - 14 y = 0

\frac{d}{d x} (\frac{x}{2 e ^{x}})

\frac{\partial}{\partial x} (15 x^{2} - 25 x y + 9 y^{2})

x \to 8 lim (5 x + ∣ x - 8 ∣)

\frac{\partial}{\partial x} (2 ln (x) + ln (y))

What is the derivative of 1/5 x^5-1/(2x^4+3x+9) ?
The derivative of 1/5 x^5-1/(2x^4+3x+9) is x^4+2/(x^5)+3
What is the first derivative of 1/5 x^5-1/(2x^4+3x+9) ?
The first derivative of 1/5 x^5-1/(2x^4+3x+9) is x^4+2/(x^5)+3