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Popular Calculus >

derivative of g(x)=3e^xsqrt(x)

Solution

derivative of

g (x) = 3 e^{x} x

Solution

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

Solution steps

\frac{d}{d x} (3 e^{x} x)

Take the constant out:

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

= 3 \frac{d}{d x} (e^{x} x)

Apply the Product Rule:

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

f = e^{x}, g = x

= 3 (\frac{d}{d x} (e^{x}) x + \frac{d}{d x} (x) e^{x})

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

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

= 3 (e^{x} x + \frac{1}{2 x} e^{x})

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

= 3 (e^{x} x + \frac{e ^{x}}{2 x})

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of g(x)=3e^xsqrt(x) ?
The derivative of g(x)=3e^xsqrt(x) is 3(e^xsqrt(x)+(e^x)/(2sqrt(x)))
What is the first derivative of g(x)=3e^xsqrt(x) ?
The first derivative of g(x)=3e^xsqrt(x) is 3(e^xsqrt(x)+(e^x)/(2sqrt(x)))