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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

\int sin (20 x) cos (15 x) d x

\int (3^{x} + \frac{2}{x}) d x

\int_{2}^{5} \frac{1}{x - 1} d x

\int x^{2} (2 x^{3} + 4)^{5} d x

\int \frac{x}{k} d x

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