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Popular >

derivative of 3/((x-4^2))

Solution

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

Solution

- \frac{6}{( x - 4 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x - 4) = 1

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

Simplify

3 (- \frac{2}{( x - 4 ) ^{3}} \cdot 1) : - \frac{6}{( x - 4 ) ^{3}}

= - \frac{6}{( x - 4 ) ^{3}}

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x \to - 3 + lim (\frac{x}{x ^{2} - 9})

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Frequently Asked Questions (FAQ)

What is the derivative of 3/((x-4^2)) ?
The derivative of 3/((x-4^2)) is -6/((x-4)^3)
What is the first derivative of 3/((x-4^2)) ?
The first derivative of 3/((x-4^2)) is -6/((x-4)^3)