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

The derivative of y=(x^2+1)((x+5+1)/x) is 2(x+6)-(6(x^2+1))/(x^2)

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

The first derivative of y=(x^2+1)((x+5+1)/x) is 2(x+6)-(6(x^2+1))/(x^2)

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derivative of

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

2 (x + 6) - \frac{6 ( x ^{2} + 1 )}{x ^{2}}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (\frac{x + 5 + 1}{x}) = - \frac{6}{x ^{2}}

= 2 x \frac{x + 5 + 1}{x} + (- \frac{6}{x ^{2}}) (x^{2} + 1)

Simplify

2 x \frac{x + 5 + 1}{x} + (- \frac{6}{x ^{2}}) (x^{2} + 1) : 2 (x + 6) - \frac{6 ( x ^{2} + 1 )}{x ^{2}}

= 2 (x + 6) - \frac{6 ( x ^{2} + 1 )}{x ^{2}}

e^{c o s^{2} (x)}

4 x^{3} + 6 x^{2} - x + 4

- 2 sin^{2} (x)

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

\frac{x}{( x ^{2} + 4 ) ^{2}}

What is the derivative of y=(x^2+1)((x+5+1)/x) ?
The derivative of y=(x^2+1)((x+5+1)/x) is 2(x+6)-(6(x^2+1))/(x^2)
What is the first derivative of y=(x^2+1)((x+5+1)/x) ?
The first derivative of y=(x^2+1)((x+5+1)/x) is 2(x+6)-(6(x^2+1))/(x^2)