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

The derivative of (2/x+x^5(x^3+1)) is 8x^7+5x^4+4x-2/(x^2)

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

The first derivative of (2/x+x^5(x^3+1)) is 8x^7+5x^4+4x-2/(x^2)

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

8 x^{7} + 5 x^{4} + 4 x - \frac{2}{x ^{2}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{2}{x} + x^{5}, g = x^{3} + 1

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

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

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

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

Simplify

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

= 8 x^{7} + 5 x^{4} + 4 x - \frac{2}{x ^{2}}

\frac{\partial}{\partial p} (arctan (pq r))

- cot (x) = \frac{v ^{'}}{v ^{2}}

\int tan^{4} (11 x) d x

\frac{\partial}{\partial z} (4 sin^{2} (z))

\int (x - \frac{1}{x}) d x

What is the derivative of (2/x+x^5(x^3+1)) ?
The derivative of (2/x+x^5(x^3+1)) is 8x^7+5x^4+4x-2/(x^2)
What is the first derivative of (2/x+x^5(x^3+1)) ?
The first derivative of (2/x+x^5(x^3+1)) is 8x^7+5x^4+4x-2/(x^2)