What is the derivative of sqrt(x)y ?

The derivative of sqrt(x)y is y/(2sqrt(x))+sqrt(x)(dy)/(dx)

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

The first derivative of sqrt(x)y is y/(2sqrt(x))+sqrt(x)(dy)/(dx)

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = y

= \frac{d}{d x} (x) y + \frac{d y}{d x} x

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

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

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

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

(4 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

(e^{- x}) (x^{2} - x)

\int \frac{( x ^{2} )}{9 + x ^{2}} d x

\frac{1}{( 1 - x )}

What is the derivative of sqrt(x)y ?
The derivative of sqrt(x)y is y/(2sqrt(x))+sqrt(x)(dy)/(dx)
What is the first derivative of sqrt(x)y ?
The first derivative of sqrt(x)y is y/(2sqrt(x))+sqrt(x)(dy)/(dx)