What is the derivative of 1/(A^2sqrt(A)) ?

The derivative of 1/(A^2sqrt(A)) is -5/(2A^{7/2)}

What is the first derivative of 1/(A^2sqrt(A)) ?

The first derivative of 1/(A^2sqrt(A)) is -5/(2A^{7/2)}

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derivative of

\frac{1}{A ^{2} A}

- \frac{5}{2 A ^{\frac{7}{2}}}

Solution steps

\frac{d}{d A} (\frac{1}{A ^{2} A})

Apply exponent rule:

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

= \frac{d}{d A} ((A^{2} A)^{- 1})

Apply the chain rule:

- \frac{1}{( A ^{2} A ) ^{2}} \frac{d}{d A} (A^{2} A)

= - \frac{1}{( A ^{2} A ) ^{2}} \frac{d}{d A} (A^{2} A)

\frac{d}{d A} (A^{2} A) = \frac{5 A ^{\frac{3}{2}}}{2}

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

Simplify

- \frac{1}{( A ^{2} A ) ^{2}} \cdot \frac{5 A ^{\frac{3}{2}}}{2} : - \frac{5}{2 A ^{\frac{7}{2}}}

= - \frac{5}{2 A ^{\frac{7}{2}}}

What is the derivative of 1/(A^2sqrt(A)) ?
The derivative of 1/(A^2sqrt(A)) is -5/(2A^{7/2)}
What is the first derivative of 1/(A^2sqrt(A)) ?
The first derivative of 1/(A^2sqrt(A)) is -5/(2A^{7/2)}