What is the derivative of sin(x+1/(sqrt(x))) ?

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

What is the first derivative of sin(x+1/(sqrt(x))) ?

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

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\frac{d}{d x} (sin (x) + \frac{1}{x})

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

Solution steps

\frac{d}{d x} (sin (x) + \frac{1}{x})

Apply the Sum/Difference Rule:

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

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

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

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

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

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