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Popular >

derivative of g(x)=5e^xsqrt(x)

Solution

derivative of

g (x) = 5 e^{x} x

Solution

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

Solution steps

\frac{d}{d x} (5 e^{x} x)

Take the constant out:

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

= 5 \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

= 5 (\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}

= 5 (e^{x} x + \frac{1}{2 x} e^{x})

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

= 5 (e^{x} x + \frac{e ^{x}}{2 x})

Popular Examples

sum from n=0 to infinity of (x-1)^n

n = 0 \sum \infty (x - 1)^{n}

limit as x approaches 0 of (x-3)/(x-3)

x \to 0 lim (\frac{x - 3}{x - 3})

derivative of ln((x^2-x^{13}))

\frac{d}{d x} (ln ((x^{2} - x)^{13}))

derivative of (x^2+2x-5/((x+1)^2))

\frac{d}{d x} (\frac{x ^{2} + 2 x - 5}{( x + 1 ) ^{2}})

integral from 0 to 2 of 2xe^{x^2}

\int_{0}^{2} 2 x e^{x^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of g(x)=5e^xsqrt(x) ?
The derivative of g(x)=5e^xsqrt(x) is 5(e^xsqrt(x)+(e^x)/(2sqrt(x)))
What is the first derivative of g(x)=5e^xsqrt(x) ?
The first derivative of g(x)=5e^xsqrt(x) is 5(e^xsqrt(x)+(e^x)/(2sqrt(x)))