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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

5 (x + \frac{1}{x})^{4} \frac{d}{d x} (x + \frac{1}{x})

= 5 (x + \frac{1}{x})^{4} \frac{d}{d x} (x + \frac{1}{x})

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

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

\frac{d}{d x} ((x)^{x})

\int_{0}^{\infty} u e^{- u^{2}} d u

\frac{s}{s ^{2} + 10 s + 9.8}

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

x \to 1 + lim (\frac{ln ( x )}{x - 1})

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