What is the derivative of 3/(sqrt(x^5)) ?

The derivative of 3/(sqrt(x^5)) is -(15)/(2x^{7/2)}

What is the first derivative of 3/(sqrt(x^5)) ?

The first derivative of 3/(sqrt(x^5)) is -(15)/(2x^{7/2)}

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\frac{d}{d x} (\frac{3}{x ^{5}})

- \frac{15}{2 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{3}{x ^{5}})

Take the constant out:

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

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

Apply exponent rule:

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

= 3 \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}

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

Simplify

3 (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}) : - \frac{15}{2 x ^{\frac{7}{2}}}

= - \frac{15}{2 x ^{\frac{7}{2}}}

x \to 2 lim ((x - 2)^{4} (5 x^{2}))

d er i v a t i v e \frac{e ^{x}}{x ^{3} + 1}

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

\int_{0}^{\infty} \frac{1}{x ^{2} - 1} d x

t a y l or (1 + x)^{(- 4)}, 0

What is the derivative of 3/(sqrt(x^5)) ?
The derivative of 3/(sqrt(x^5)) is -(15)/(2x^{7/2)}
What is the first derivative of 3/(sqrt(x^5)) ?
The first derivative of 3/(sqrt(x^5)) is -(15)/(2x^{7/2)}