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

The derivative of (x^2+1*(x+5+1/x)) is 3x^2+10x-1/(x^2)+2

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

The first derivative of (x^2+1*(x+5+1/x)) is 3x^2+10x-1/(x^2)+2

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

3 x^{2} + 10 x - \frac{1}{x ^{2}} + 2

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x + 5 + \frac{1}{x}) + (- \frac{1}{x ^{2}} + 1) (x^{2} + 1) : 3 x^{2} + 10 x - \frac{1}{x ^{2}} + 2

= 3 x^{2} + 10 x - \frac{1}{x ^{2}} + 2

What is the derivative of (x^2+1*(x+5+1/x)) ?
The derivative of (x^2+1*(x+5+1/x)) is 3x^2+10x-1/(x^2)+2
What is the first derivative of (x^2+1*(x+5+1/x)) ?
The first derivative of (x^2+1*(x+5+1/x)) is 3x^2+10x-1/(x^2)+2