How do you differentiate $y=e^x+x^10-1/x$ ?

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Answer 1 · 2017-08-01T03:59:31

$color(blue)(y'(x) = e^x + 10x^9 + 1/(x^2)$

We're asked to find the derivative

$(dy)/(dx) [y = e^x + x^10 - 1/x]$

The derivative of $e^x$ is defined as $e^x$ :

$y'(x) = e^x + d/(dx)[x^10] - d/(dx)[1/x]$

Us the power rule on the $x^10$ term:

$y'(x) = e^x + 10x^9 - d/(dx)[1/x]$

Use the quotient rule on the $1/x$ term, which states

$d/(dx)[u/v] = (v(du)/(dx) - u(dv)/(dx))/(v^2)$

where

$y'(x) = e^x + 10x^9 - (xd/(dx)[1] - 1d/(dx)[x])/(x^2)$

The derivative of $1$ is $0$ and the derivative of $x$ is $1$ :

$color(blue)(y'(x) = e^x + 10x^9 + 1/(x^2)$

How do you differentiate y=e^x+x^10-1/xy=e^x+x^10-1/x?