What is the derivative of sqrt(xsin(x)) ?

The derivative of sqrt(xsin(x)) is (sin(x)+xcos(x))/(2sqrt(xsin(x)))

What is the first derivative of sqrt(xsin(x)) ?

The first derivative of sqrt(xsin(x)) is (sin(x)+xcos(x))/(2sqrt(xsin(x)))

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

\frac{sin ( x ) + x cos ( x )}{2 x sin ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x e ^{x}}{( x + 1 ) ^{2}} d x

\frac{d}{d x} ((5 x^{2} - 8 x) e^{x})

x^{^{''}} - 0 x^{^{'}} + x = 0

\int 6 d x

\frac{\partial}{\partial y} (\frac{- y}{x ^{2} + y ^{2}})

What is the derivative of sqrt(xsin(x)) ?
The derivative of sqrt(xsin(x)) is (sin(x)+xcos(x))/(2sqrt(xsin(x)))
What is the first derivative of sqrt(xsin(x)) ?
The first derivative of sqrt(xsin(x)) is (sin(x)+xcos(x))/(2sqrt(xsin(x)))