What is the derivative of (x^2(e^x+5)/(e^xsqrt(x))) ?

The derivative of (x^2(e^x+5)/(e^xsqrt(x))) is (sqrt(x)(-10x+3e^x+15))/(2e^x)

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

The first derivative of (x^2(e^x+5)/(e^xsqrt(x))) is (sqrt(x)(-10x+3e^x+15))/(2e^x)

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

\frac{x ( - 10 x + 3 e ^{x} + 15 )}{2 e ^{x}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{( 2 x ( e ^{x} + 5 ) + e ^{x} x ^{2} ) e ^{x} x - ( e ^{x} x + \frac{e ^{x}}{2 x} ) x ^{2} ( e ^{x} + 5 )}{( e ^{x} x ) ^{2}} : \frac{x ( - 10 x + 3 e ^{x} + 15 )}{2 e ^{x}}

= \frac{x ( - 10 x + 3 e ^{x} + 15 )}{2 e ^{x}}

\frac{d}{d x} (7^{x} + 7 cos (\frac{7 x}{2}))

x^{2} y^{^{''}} - x y^{^{'}} + y = 0

\int_{1}^{e^{5}} \frac{1}{x ( 1 + ln ( x ) )} d x

\int - sin^{4} (x) d x

\int \frac{x ^{2} - 3 x - 5}{x} d x

What is the derivative of (x^2(e^x+5)/(e^xsqrt(x))) ?
The derivative of (x^2(e^x+5)/(e^xsqrt(x))) is (sqrt(x)(-10x+3e^x+15))/(2e^x)
What is the first derivative of (x^2(e^x+5)/(e^xsqrt(x))) ?
The first derivative of (x^2(e^x+5)/(e^xsqrt(x))) is (sqrt(x)(-10x+3e^x+15))/(2e^x)