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Popular >

derivative of e^{3x}-6/(sqrt(x))

Solution

\frac{d}{d x} (e^{3 x} - \frac{6}{x})

Solution

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

Solution steps

\frac{d}{d x} (e^{3 x} - \frac{6}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{3 x}) - \frac{d}{d x} (\frac{6}{x})

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

\frac{d}{d x} (\frac{6}{x}) = - \frac{3}{x ^{\frac{3}{2}}}

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

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of e^{3x}-6/(sqrt(x)) ?
The derivative of e^{3x}-6/(sqrt(x)) is 3e^{3x}+3/(x^{3/2)}
What is the first derivative of e^{3x}-6/(sqrt(x)) ?
The first derivative of e^{3x}-6/(sqrt(x)) is 3e^{3x}+3/(x^{3/2)}