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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derivative of

\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

\int \frac{4 x + 1}{4 x ^{2} + 2 x + 3} d x

2 t \cdot \frac{d y}{d t} + 5 y = t

y = \frac{8 x}{e ^{x}}

x \to 1 lim (e^{5 x^{3} - 5 x})

\int_{0}^{6} \frac{2 x}{( x - 7 ) ^{2}} d x

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