What is the derivative of f(x)=(4x-7)/(28x^5) ?

The derivative of f(x)=(4x-7)/(28x^5) is (-16x+35)/(28x^6)

What is the first derivative of f(x)=(4x-7)/(28x^5) ?

The first derivative of f(x)=(4x-7)/(28x^5) is (-16x+35)/(28x^6)

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derivative of

f (x) = \frac{4 x - 7}{28 x ^{5}}

\frac{- 16 x + 35}{28 x ^{6}}

Solution steps

\frac{d}{d x} (\frac{4 x - 7}{28 x ^{5}})

Take the constant out:

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

= \frac{1}{28} \frac{d}{d x} (\frac{4 x - 7}{x ^{5}})

Apply the Quotient Rule:

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

= \frac{1}{28} \cdot \frac{\frac{d}{d x} ( 4 x - 7 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( 4 x - 7 )}{( x ^{5} ) ^{2}}

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

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

= \frac{1}{28} \cdot \frac{4 x ^{5} - 5 x ^{4} ( 4 x - 7 )}{( x ^{5} ) ^{2}}

Simplify

\frac{1}{28} \cdot \frac{4 x ^{5} - 5 x ^{4} ( 4 x - 7 )}{( x ^{5} ) ^{2}} : \frac{- 16 x + 35}{28 x ^{6}}

= \frac{- 16 x + 35}{28 x ^{6}}

What is the derivative of f(x)=(4x-7)/(28x^5) ?
The derivative of f(x)=(4x-7)/(28x^5) is (-16x+35)/(28x^6)
What is the first derivative of f(x)=(4x-7)/(28x^5) ?
The first derivative of f(x)=(4x-7)/(28x^5) is (-16x+35)/(28x^6)