What is (\partial)/(\partial x)(9e^xsqrt(x)) ?

The answer to (\partial)/(\partial x)(9e^xsqrt(x)) is 9(e^xsqrt(x)+(e^x)/(2sqrt(x)))

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(\partial)/(\partial x)(9e^xsqrt(x))

\frac{\partial}{\partial x} (9 e^{x} x)

9 (e^{x} x + \frac{e ^{x}}{2 x})

Solution steps

\frac{\partial}{\partial x} (9 e^{x} x)

Take the constant out:

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

= 9 \frac{\partial}{\partial x} (e^{x} x)

Apply the Product Rule:

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

f = e^{x}, g = x

= 9 (\frac{\partial}{\partial x} (e^{x}) x + \frac{\partial}{\partial x} (x) e^{x})

\frac{\partial}{\partial x} (e^{x}) = e^{x}

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

= 9 (e^{x} x + \frac{1}{2 x} e^{x})

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

= 9 (e^{x} x + \frac{e ^{x}}{2 x})

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What is (\partial)/(\partial x)(9e^xsqrt(x)) ?
The answer to (\partial)/(\partial x)(9e^xsqrt(x)) is 9(e^xsqrt(x)+(e^x)/(2sqrt(x)))