What is the derivative of 5/((x-6^2)) ?

The derivative of 5/((x-6^2)) is -(10)/((x-6)^3)

What is the first derivative of 5/((x-6^2)) ?

The first derivative of 5/((x-6^2)) is -(10)/((x-6)^3)

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\frac{d}{d x} (\frac{5}{( x - 6 ) ^{2}})

- \frac{10}{( x - 6 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{5}{( x - 6 ) ^{2}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{( x - 6 ) ^{2}})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((x - 6)^{- 2})

Apply the chain rule:

- \frac{2}{( x - 6 ) ^{3}} \frac{d}{d x} (x - 6)

= - \frac{2}{( x - 6 ) ^{3}} \frac{d}{d x} (x - 6)

\frac{d}{d x} (x - 6) = 1

= 5 (- \frac{2}{( x - 6 ) ^{3}} \cdot 1)

Simplify

5 (- \frac{2}{( x - 6 ) ^{3}} \cdot 1) : - \frac{10}{( x - 6 ) ^{3}}

= - \frac{10}{( x - 6 ) ^{3}}

\int_{\frac{1}{5}}^{3} 8 x ln (5 x) d x

ln (e)

\int x^{\frac{3}{4}} d x

y^{^{''}} + 289 y = sec (17 x)

f (x) = 2 x^{5} - 3 e^{6 x}

What is the derivative of 5/((x-6^2)) ?
The derivative of 5/((x-6^2)) is -(10)/((x-6)^3)
What is the first derivative of 5/((x-6^2)) ?
The first derivative of 5/((x-6^2)) is -(10)/((x-6)^3)