What is the derivative of (10)/((x^2-7)^4) ?

The derivative of (10)/((x^2-7)^4) is -(80x)/((x^2-7)^5)

What is the first derivative of (10)/((x^2-7)^4) ?

The first derivative of (10)/((x^2-7)^4) is -(80x)/((x^2-7)^5)

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derivative of

\frac{10}{( x ^{2} - 7 ) ^{4}}

- \frac{80 x}{( x ^{2} - 7 ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{10}{( x ^{2} - 7 ) ^{4}})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{1}{( x ^{2} - 7 ) ^{4}})

Apply exponent rule:

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

= 10 \frac{d}{d x} ((x^{2} - 7)^{- 4})

Apply the chain rule:

- \frac{4}{( x ^{2} - 7 ) ^{5}} \frac{d}{d x} (x^{2} - 7)

= - \frac{4}{( x ^{2} - 7 ) ^{5}} \frac{d}{d x} (x^{2} - 7)

\frac{d}{d x} (x^{2} - 7) = 2 x

= 10 (- \frac{4}{( x ^{2} - 7 ) ^{5}} \cdot 2 x)

Simplify

10 (- \frac{4}{( x ^{2} - 7 ) ^{5}} \cdot 2 x) : - \frac{80 x}{( x ^{2} - 7 ) ^{5}}

= - \frac{80 x}{( x ^{2} - 7 ) ^{5}}

y = sec (x), (\frac{π}{3}, 2)

\frac{7}{6 s ( s + \frac{2}{9} )}

\int ln (x + 9) d x

\int e^{2} d x

\frac{d}{d x} ((9 x + 8) x^{2})

What is the derivative of (10)/((x^2-7)^4) ?
The derivative of (10)/((x^2-7)^4) is -(80x)/((x^2-7)^5)
What is the first derivative of (10)/((x^2-7)^4) ?
The first derivative of (10)/((x^2-7)^4) is -(80x)/((x^2-7)^5)