What is the derivative of f(x)=(19)/(sqrt(x^5)) ?

The derivative of f(x)=(19)/(sqrt(x^5)) is -(95x^4)/(2(x^5)^{3/2)}

What is the first derivative of f(x)=(19)/(sqrt(x^5)) ?

The first derivative of f(x)=(19)/(sqrt(x^5)) is -(95x^4)/(2(x^5)^{3/2)}

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derivative of

f (x) = \frac{19}{x ^{5}}

- \frac{95 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{19}{x ^{5}})

Take the constant out:

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

= 19 \frac{d}{d x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= 19 \frac{d}{d x} ((x^{5})^{- \frac{1}{2}})

Apply the chain rule:

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 19 (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4})

Simplify

19 (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}) : - \frac{95 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

= - \frac{95 x ^{4}}{2 ( x ^{5} ) ^{\frac{3}{2}}}

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What is the derivative of f(x)=(19)/(sqrt(x^5)) ?
The derivative of f(x)=(19)/(sqrt(x^5)) is -(95x^4)/(2(x^5)^{3/2)}
What is the first derivative of f(x)=(19)/(sqrt(x^5)) ?
The first derivative of f(x)=(19)/(sqrt(x^5)) is -(95x^4)/(2(x^5)^{3/2)}