What is the derivative of (5e^xx^{3/2})/2+e^xx^{5/2} ?

The derivative of (5e^xx^{3/2})/2+e^xx^{5/2} is (20e^xx^{3/2}+15e^xx^{1/2}+4e^xx^{5/2})/4

What is the first derivative of (5e^xx^{3/2})/2+e^xx^{5/2} ?

The first derivative of (5e^xx^{3/2})/2+e^xx^{5/2} is (20e^xx^{3/2}+15e^xx^{1/2}+4e^xx^{5/2})/4

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derivative of

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

\frac{20 e ^{x} x ^{\frac{3}{2}} + 15 e ^{x} x ^{\frac{1}{2}} + 4 e ^{x} x ^{\frac{5}{2}}}{4}

Solution steps

\frac{d}{d x} (\frac{5 e ^{x} x ^{\frac{3}{2}}}{2} + e^{x} x^{\frac{5}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{5 e ^{x} x ^{\frac{3}{2}}}{2}) + \frac{d}{d x} (e^{x} x^{\frac{5}{2}})

\frac{d}{d x} (\frac{5 e ^{x} x ^{\frac{3}{2}}}{2}) = \frac{5}{2} (e^{x} x^{\frac{3}{2}} + \frac{3 e ^{x} x ^{\frac{1}{2}}}{2})

\frac{d}{d x} (e^{x} x^{\frac{5}{2}}) = e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2}

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

Simplify

\frac{5}{2} (e^{x} x^{\frac{3}{2}} + \frac{3 e ^{x} x ^{\frac{1}{2}}}{2}) + e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2} : \frac{20 e ^{x} x ^{\frac{3}{2}} + 15 e ^{x} x ^{\frac{1}{2}} + 4 e ^{x} x ^{\frac{5}{2}}}{4}

= \frac{20 e ^{x} x ^{\frac{3}{2}} + 15 e ^{x} x ^{\frac{1}{2}} + 4 e ^{x} x ^{\frac{5}{2}}}{4}

2 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 6 x e^{- y}

\int 3 e^{5} d x

\frac{d}{d x} (\frac{1 + tan ^{2} ( x )}{x sec ( x )})

\int ln (sec (x)) d x

\frac{1}{s ^{2} ( s ^{2} + 3 s + 2 )}

What is the derivative of (5e^xx^{3/2})/2+e^xx^{5/2} ?
The derivative of (5e^xx^{3/2})/2+e^xx^{5/2} is (20e^xx^{3/2}+15e^xx^{1/2}+4e^xx^{5/2})/4
What is the first derivative of (5e^xx^{3/2})/2+e^xx^{5/2} ?
The first derivative of (5e^xx^{3/2})/2+e^xx^{5/2} is (20e^xx^{3/2}+15e^xx^{1/2}+4e^xx^{5/2})/4