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

The derivative of (x^4)/2-2/(x^4)+6sqrt(x) is (8+3x^{9/2}+2x^8)/(x^{9/2)sqrt(x)}

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

The first derivative of (x^4)/2-2/(x^4)+6sqrt(x) is (8+3x^{9/2}+2x^8)/(x^{9/2)sqrt(x)}

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derivative of

\frac{x ^{4}}{2} - \frac{2}{x ^{4}} + 6 x

\frac{8 + 3 x ^{\frac{9}{2}} + 2 x ^{8}}{x ^{\frac{9}{2}} x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{x ^{4}}{2}) = 2 x^{3}

\frac{d}{d x} (\frac{2}{x ^{4}}) = - \frac{8}{x ^{5}}

\frac{d}{d x} (6 x) = \frac{3}{x}

= 2 x^{3} - (- \frac{8}{x ^{5}}) + \frac{3}{x}

Simplify

2 x^{3} - (- \frac{8}{x ^{5}}) + \frac{3}{x} : \frac{8 + 3 x ^{\frac{9}{2}} + 2 x ^{8}}{x ^{\frac{9}{2}} x}

= \frac{8 + 3 x ^{\frac{9}{2}} + 2 x ^{8}}{x ^{\frac{9}{2}} x}

\frac{d}{d x} (arcsin (5 x - 1))

\int_{- 2}^{0} \frac{5}{x ^{2} + 4 x + 8} d x

x \to 4 lim (- x^{2} + 3 x - 7)

\frac{d}{d x} (\frac{π}{5})

\int x^{2} + 2 x - 15 d x

What is the derivative of (x^4)/2-2/(x^4)+6sqrt(x) ?
The derivative of (x^4)/2-2/(x^4)+6sqrt(x) is (8+3x^{9/2}+2x^8)/(x^{9/2)sqrt(x)}
What is the first derivative of (x^4)/2-2/(x^4)+6sqrt(x) ?
The first derivative of (x^4)/2-2/(x^4)+6sqrt(x) is (8+3x^{9/2}+2x^8)/(x^{9/2)sqrt(x)}