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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 1 + lim ((x - 3)^{2})

y^{^{''}} - 4 y^{^{'}} + 29 y = 0

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

\frac{d}{d x} (x e^{x y + 1})

f (x) = x^{2} - 3 x + 2, at x = 2

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