What is the derivative of f(x)=(4x)/((x-9)^5) ?

The derivative of f(x)=(4x)/((x-9)^5) is (4(-9-4x))/((x-9)^6)

What is the first derivative of f(x)=(4x)/((x-9)^5) ?

The first derivative of f(x)=(4x)/((x-9)^5) is (4(-9-4x))/((x-9)^6)

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derivative of

f (x) = \frac{4 x}{( x - 9 ) ^{5}}

\frac{4 ( - 9 - 4 x )}{( x - 9 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{4 x}{( x - 9 ) ^{5}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x}{( x - 9 ) ^{5}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 4 \cdot \frac{\frac{d x}{d x} ( x - 9 ) ^{5} - \frac{d}{d x} ( ( x - 9 ) ^{5} ) x}{( ( x - 9 ) ^{5} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 9)^{5}) = 5 (x - 9)^{4}

= 4 \cdot \frac{1 \cdot ( x - 9 ) ^{5} - 5 ( x - 9 ) ^{4} x}{( ( x - 9 ) ^{5} ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( x - 9 ) ^{5} - 5 ( x - 9 ) ^{4} x}{( ( x - 9 ) ^{5} ) ^{2}} : \frac{4 ( - 9 - 4 x )}{( x - 9 ) ^{6}}

= \frac{4 ( - 9 - 4 x )}{( x - 9 ) ^{6}}

What is the derivative of f(x)=(4x)/((x-9)^5) ?
The derivative of f(x)=(4x)/((x-9)^5) is (4(-9-4x))/((x-9)^6)
What is the first derivative of f(x)=(4x)/((x-9)^5) ?
The first derivative of f(x)=(4x)/((x-9)^5) is (4(-9-4x))/((x-9)^6)