What is the derivative of 1/(sqrt(x))*3e^x ?

The derivative of 1/(sqrt(x))*3e^x is 3(-(e^x)/(2x^{3/2)}+(e^x)/(sqrt(x)))

What is the first derivative of 1/(sqrt(x))*3e^x ?

The first derivative of 1/(sqrt(x))*3e^x is 3(-(e^x)/(2x^{3/2)}+(e^x)/(sqrt(x)))

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derivative of

\frac{1}{x} \cdot 3 e^{x}

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

Solution steps

\frac{d}{d x} (\frac{1}{x} \cdot 3 e^{x})

Take the constant out:

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

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

Apply the Product Rule:

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

f = \frac{1}{x}, g = e^{x}

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

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{2 x ^{\frac{3}{2}}}

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

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

Simplify

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

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

\int \frac{1}{9 x ^{2} - 4} d x

\int \frac{1}{2 x + x ^{3}} d x

\int \frac{1}{x 64 x ^{4} - 1} d x

\frac{d}{d x} (\frac{1}{( x ^{3} - 2 x ^{2} + 7 ) ^{4}})

What is the derivative of 1/(sqrt(x))*3e^x ?
The derivative of 1/(sqrt(x))*3e^x is 3(-(e^x)/(2x^{3/2)}+(e^x)/(sqrt(x)))
What is the first derivative of 1/(sqrt(x))*3e^x ?
The first derivative of 1/(sqrt(x))*3e^x is 3(-(e^x)/(2x^{3/2)}+(e^x)/(sqrt(x)))