What is (\partial)/(\partial x)(ysqrt(x)) ?

The answer to (\partial)/(\partial x)(ysqrt(x)) is y/(2sqrt(x))

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(\partial)/(\partial x)(ysqrt(x))

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

\frac{y}{2 x}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (x)

Apply radical rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{y}{2 x}

\frac{\partial}{\partial x} (e^{- \frac{π}{2}})

\int 20 t e^{t} d t

f (x) = 4 x^{2} + 7, (- 3, 43)

(- 4, - 6), (4, - 2)

f (x) = \frac{- 4 x}{x ^{2} + 1}, (1, - 2)

What is (\partial)/(\partial x)(ysqrt(x)) ?
The answer to (\partial)/(\partial x)(ysqrt(x)) is y/(2sqrt(x))