What is the derivative of f(x)=x^2-2/x+3*sin(2x) ?

The derivative of f(x)=x^2-2/x+3*sin(2x) is 2x+2/(x^2)+6cos(2x)

What is the first derivative of f(x)=x^2-2/x+3*sin(2x) ?

The first derivative of f(x)=x^2-2/x+3*sin(2x) is 2x+2/(x^2)+6cos(2x)

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derivative

2 x + \frac{2}{x ^{2}} + 6 cos (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (3 sin (2 x)) = 6 cos (2 x)

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

Simplify

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

What is the derivative of f(x)=x^2-2/x+3*sin(2x) ?
The derivative of f(x)=x^2-2/x+3*sin(2x) is 2x+2/(x^2)+6cos(2x)
What is the first derivative of f(x)=x^2-2/x+3*sin(2x) ?
The first derivative of f(x)=x^2-2/x+3*sin(2x) is 2x+2/(x^2)+6cos(2x)