What is the derivative of 0.09e^xsqrt(x) ?

The derivative of 0.09e^xsqrt(x) is 0.09(e^xsqrt(x)+(0.5e^x)/(sqrt(x)))

What is the first derivative of 0.09e^xsqrt(x) ?

The first derivative of 0.09e^xsqrt(x) is 0.09(e^xsqrt(x)+(0.5e^x)/(sqrt(x)))

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derivative of

0.09 e^{x} x

0.09 (e^{x} x + \frac{0.5 e ^{x}}{x})

Solution steps

\frac{d}{d x} (0.09 e^{x} x)

Take the constant out:

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

= 0.09 \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

= 0.09 (\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}

= 0.09 (e^{x} x + \frac{1}{2 x} e^{x})

Simplify

0.09 (e^{x} x + \frac{1}{2 x} e^{x}) : 0.09 (e^{x} x + \frac{0.5 e ^{x}}{x})

= 0.09 (e^{x} x + \frac{0.5 e ^{x}}{x})

What is the derivative of 0.09e^xsqrt(x) ?
The derivative of 0.09e^xsqrt(x) is 0.09(e^xsqrt(x)+(0.5e^x)/(sqrt(x)))
What is the first derivative of 0.09e^xsqrt(x) ?
The first derivative of 0.09e^xsqrt(x) is 0.09(e^xsqrt(x)+(0.5e^x)/(sqrt(x)))