What is the derivative of x^{1/2}*csc(xsin(x)) ?

The derivative of x^{1/2}*csc(xsin(x)) is 1/(2x^{1/2)}

What is the first derivative of x^{1/2}*csc(xsin(x)) ?

The first derivative of x^{1/2}*csc(xsin(x)) is 1/(2x^{1/2)}

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\frac{d}{d x} (x^{\frac{1}{2}} \cdot csc (x) sin (x))

\frac{1}{2 x ^{\frac{1}{2}}}

Solution steps

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

Simplify

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

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

Apply the Power Rule:

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

= \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

\frac{1}{2} x^{\frac{1}{2} - 1} : \frac{1}{2 x ^{\frac{1}{2}}}

= \frac{1}{2 x ^{\frac{1}{2}}}

What is the derivative of x^{1/2}*csc(xsin(x)) ?
The derivative of x^{1/2}*csc(xsin(x)) is 1/(2x^{1/2)}
What is the first derivative of x^{1/2}*csc(xsin(x)) ?
The first derivative of x^{1/2}*csc(xsin(x)) is 1/(2x^{1/2)}