What is the derivative of 2xe^x-1/(sqrt(x)) ?

The derivative of 2xe^x-1/(sqrt(x)) is (1+4e^xx^{3/2}+4e^xx^{5/2})/(2x^{3/2)}

What is the first derivative of 2xe^x-1/(sqrt(x)) ?

The first derivative of 2xe^x-1/(sqrt(x)) is (1+4e^xx^{3/2}+4e^xx^{5/2})/(2x^{3/2)}

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

\frac{1 + 4 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{5}{2}}}{2 x ^{\frac{3}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

2 (e^{x} + e^{x} x) - (- \frac{1}{2 x ^{\frac{3}{2}}}) : \frac{1 + 4 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{5}{2}}}{2 x ^{\frac{3}{2}}}

= \frac{1 + 4 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{5}{2}}}{2 x ^{\frac{3}{2}}}

\int \frac{21}{1 - cos ( 3 x )} d x

\frac{d}{d x} (cot (2 x^{4} - 3 x^{2} - 4))

x \frac{d y}{d x} + 4 y = x^{3} - x

\int 2 tan (x) sec^{4} (x) d x

8 x e^{x}

What is the derivative of 2xe^x-1/(sqrt(x)) ?
The derivative of 2xe^x-1/(sqrt(x)) is (1+4e^xx^{3/2}+4e^xx^{5/2})/(2x^{3/2)}
What is the first derivative of 2xe^x-1/(sqrt(x)) ?
The first derivative of 2xe^x-1/(sqrt(x)) is (1+4e^xx^{3/2}+4e^xx^{5/2})/(2x^{3/2)}