What is the derivative of (7e^xx^{5/2})/2+e^xx^{7/2} ?

The derivative of (7e^xx^{5/2})/2+e^xx^{7/2} is (28e^xx^{5/2}+35e^xx^{3/2}+4e^xx^{7/2})/4

What is the first derivative of (7e^xx^{5/2})/2+e^xx^{7/2} ?

The first derivative of (7e^xx^{5/2})/2+e^xx^{7/2} is (28e^xx^{5/2}+35e^xx^{3/2}+4e^xx^{7/2})/4

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derivative of

\frac{7 e ^{x} x ^{\frac{5}{2}}}{2} + e^{x} x^{\frac{7}{2}}

\frac{28 e ^{x} x ^{\frac{5}{2}} + 35 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{7}{2}}}{4}

Solution steps

\frac{d}{d x} (\frac{7 e ^{x} x ^{\frac{5}{2}}}{2} + e^{x} x^{\frac{7}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{7 e ^{x} x ^{\frac{5}{2}}}{2}) + \frac{d}{d x} (e^{x} x^{\frac{7}{2}})

\frac{d}{d x} (\frac{7 e ^{x} x ^{\frac{5}{2}}}{2}) = \frac{7}{2} (e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2})

\frac{d}{d x} (e^{x} x^{\frac{7}{2}}) = e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2}

= \frac{7}{2} (e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2}) + e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2}

Simplify

\frac{7}{2} (e^{x} x^{\frac{5}{2}} + \frac{5 e ^{x} x ^{\frac{3}{2}}}{2}) + e^{x} x^{\frac{7}{2}} + \frac{7 e ^{x} x ^{\frac{5}{2}}}{2} : \frac{28 e ^{x} x ^{\frac{5}{2}} + 35 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{7}{2}}}{4}

= \frac{28 e ^{x} x ^{\frac{5}{2}} + 35 e ^{x} x ^{\frac{3}{2}} + 4 e ^{x} x ^{\frac{7}{2}}}{4}

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x \to - 3 lim ((5 - x)^{\frac{4}{3}})

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What is the derivative of (7e^xx^{5/2})/2+e^xx^{7/2} ?
The derivative of (7e^xx^{5/2})/2+e^xx^{7/2} is (28e^xx^{5/2}+35e^xx^{3/2}+4e^xx^{7/2})/4
What is the first derivative of (7e^xx^{5/2})/2+e^xx^{7/2} ?
The first derivative of (7e^xx^{5/2})/2+e^xx^{7/2} is (28e^xx^{5/2}+35e^xx^{3/2}+4e^xx^{7/2})/4