What is the derivative of x^{1/2}y ?

The derivative of x^{1/2}y is (y+2x\frac{dy)/(dx)}{2x^{1/2}}

What is the first derivative of x^{1/2}y ?

The first derivative of x^{1/2}y is (y+2x\frac{dy)/(dx)}{2x^{1/2}}

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

\frac{y + 2 x \frac{d y}{d x}}{2 x ^{\frac{1}{2}}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{1}{2}}, g = y

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

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

= \frac{1}{2 x ^{\frac{1}{2}}} y + \frac{d y}{d x} x^{\frac{1}{2}}

Simplify

\frac{1}{2 x ^{\frac{1}{2}}} y + \frac{d y}{d x} x^{\frac{1}{2}} : \frac{y + 2 x \frac{d y}{d x}}{2 x ^{\frac{1}{2}}}

= \frac{y + 2 x \frac{d y}{d x}}{2 x ^{\frac{1}{2}}}

r \cdot \frac{d q}{d r} + 3 q = 0

x \to 0 + lim (5 x + 6)

\int \frac{4 x sin ( y ^{2} )}{y ^{3}} d y

x \to - 1 lim (x + 1)

x \to - 3 lim (\frac{2}{( x + 3 ) ^{6}})

What is the derivative of x^{1/2}y ?
The derivative of x^{1/2}y is (y+2x\frac{dy)/(dx)}{2x^{1/2}}
What is the first derivative of x^{1/2}y ?
The first derivative of x^{1/2}y is (y+2x\frac{dy)/(dx)}{2x^{1/2}}