What is the derivative of 6sqrt(x)e^x ?

The derivative of 6sqrt(x)e^x is 6((e^x)/(2sqrt(x))+e^xsqrt(x))

What is the first derivative of 6sqrt(x)e^x ?

The first derivative of 6sqrt(x)e^x is 6((e^x)/(2sqrt(x))+e^xsqrt(x))

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derivative of

6 x e^{x}

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

Solution steps

\frac{d}{d x} (6 x e^{x})

Take the constant out:

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

= 6 \frac{d}{d x} (x e^{x})

Apply the Product Rule:

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

f = x, g = e^{x}

= 6 (\frac{d}{d x} (x) e^{x} + \frac{d}{d x} (e^{x}) x)

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

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

= 6 (\frac{1}{2 x} e^{x} + e^{x} x)

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

= 6 (\frac{e ^{x}}{2 x} + e^{x} x)

\int \frac{1}{( 4 - x ^{2} )} d x

\int \frac{x ^{\frac{3}{2}}}{x} d x

\int e^{- s t} t d t

f (x) = 2 x^{3} - x^{2} + 9, at x = 2

x \to \infty lim (- \frac{π}{2})

What is the derivative of 6sqrt(x)e^x ?
The derivative of 6sqrt(x)e^x is 6((e^x)/(2sqrt(x))+e^xsqrt(x))
What is the first derivative of 6sqrt(x)e^x ?
The first derivative of 6sqrt(x)e^x is 6((e^x)/(2sqrt(x))+e^xsqrt(x))