What is the derivative of f(x)=-(12)/((x-6)^2) ?

The derivative of f(x)=-(12)/((x-6)^2) is (24)/((x-6)^3)

What is the first derivative of f(x)=-(12)/((x-6)^2) ?

The first derivative of f(x)=-(12)/((x-6)^2) is (24)/((x-6)^3)

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derivative of

f (x) = - \frac{12}{( x - 6 ) ^{2}}

\frac{24}{( x - 6 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{12}{( x - 6 ) ^{2}})

Take the constant out:

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

= - 12 \frac{d}{d x} (\frac{1}{( x - 6 ) ^{2}})

Apply exponent rule:

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

= - 12 \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

= - 12 (- \frac{2}{( x - 6 ) ^{3}} \cdot 1)

Simplify

- 12 (- \frac{2}{( x - 6 ) ^{3}} \cdot 1) : \frac{24}{( x - 6 ) ^{3}}

= \frac{24}{( x - 6 ) ^{3}}

\int \frac{5 x ^{3} + 3 x}{x - 1} d x

\int (x^{5} + 1) d x

y^{^{''}} + 8 y^{^{'}} - 9 y = e^{3 x}

\frac{d}{d x} (x (x - 21)^{2})

\frac{( e ^{- 2 s} )}{s + 1}

What is the derivative of f(x)=-(12)/((x-6)^2) ?
The derivative of f(x)=-(12)/((x-6)^2) is (24)/((x-6)^3)
What is the first derivative of f(x)=-(12)/((x-6)^2) ?
The first derivative of f(x)=-(12)/((x-6)^2) is (24)/((x-6)^3)