What is the derivative of 10sqrt(x)*e^x ?

The derivative of 10sqrt(x)*e^x is 10((e^x)/(2sqrt(x))+e^xsqrt(x))

What is the first derivative of 10sqrt(x)*e^x ?

The first derivative of 10sqrt(x)*e^x is 10((e^x)/(2sqrt(x))+e^xsqrt(x))

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derivative of

10 x \cdot e^{x}

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

Solution steps

\frac{d}{d x} (10 x e^{x})

Take the constant out:

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

= 10 \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}

= 10 (\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}

= 10 (\frac{1}{2 x} e^{x} + e^{x} x)

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

= 10 (\frac{e ^{x}}{2 x} + e^{x} x)

\int_{0}^{1} 1.5 x^{2} d x

\frac{\partial}{\partial s} (2 s^{2} t^{2})

\frac{d}{d x} (\frac{x}{11} - \frac{11}{x})

\frac{d}{d x} (2 x + \frac{1}{ln ( x ^{2} + e ) + 1} - 4)

What is the derivative of 10sqrt(x)*e^x ?
The derivative of 10sqrt(x)*e^x is 10((e^x)/(2sqrt(x))+e^xsqrt(x))
What is the first derivative of 10sqrt(x)*e^x ?
The first derivative of 10sqrt(x)*e^x is 10((e^x)/(2sqrt(x))+e^xsqrt(x))