What is the derivative of-sin(x+cos(x)+x-1/(x^2)) ?

The derivative of-sin(x+cos(x)+x-1/(x^2)) is -cos(x)-sin(x)+1+2/(x^3)

What is the first derivative of-sin(x+cos(x)+x-1/(x^2)) ?

The first derivative of-sin(x+cos(x)+x-1/(x^2)) is -cos(x)-sin(x)+1+2/(x^3)

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

- cos (x) - sin (x) + 1 + \frac{2}{x ^{3}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (cos (x)) = - sin (x)

\frac{d x}{d x} = 1

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

= - cos (x) - sin (x) + 1 - (- \frac{2}{x ^{3}})

Simplify

= - cos (x) - sin (x) + 1 + \frac{2}{x ^{3}}

What is the derivative of-sin(x+cos(x)+x-1/(x^2)) ?
The derivative of-sin(x+cos(x)+x-1/(x^2)) is -cos(x)-sin(x)+1+2/(x^3)
What is the first derivative of-sin(x+cos(x)+x-1/(x^2)) ?
The first derivative of-sin(x+cos(x)+x-1/(x^2)) is -cos(x)-sin(x)+1+2/(x^3)