What is the derivative of f(x)=(7x-5)/(x^2+4x) ?

The derivative of f(x)=(7x-5)/(x^2+4x) is (-7x^2+10x+20)/((x^2+4x)^2)

What is the first derivative of f(x)=(7x-5)/(x^2+4x) ?

The first derivative of f(x)=(7x-5)/(x^2+4x) is (-7x^2+10x+20)/((x^2+4x)^2)

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derivative of

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

\frac{- 7 x ^{2} + 10 x + 20}{( x ^{2} + 4 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2} + 4 x) = 2 x + 4

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

Expand

7 (x^{2} + 4 x) - (2 x + 4) (7 x - 5) : - 7 x^{2} + 10 x + 20

= \frac{- 7 x ^{2} + 10 x + 20}{( x ^{2} + 4 x ) ^{2}}

f (x) = x^{4} + 4 x^{3} - 48 x^{2} + 6

\int_{0}^{9} 2 x d x

\int_{0}^{\frac{π}{3}} sec^{2} (x) d x

- 4 x^{2} + 12 x, 2 x^{2} - 5

x \to - 3 lim (10 x - 4)

What is the derivative of f(x)=(7x-5)/(x^2+4x) ?
The derivative of f(x)=(7x-5)/(x^2+4x) is (-7x^2+10x+20)/((x^2+4x)^2)
What is the first derivative of f(x)=(7x-5)/(x^2+4x) ?
The first derivative of f(x)=(7x-5)/(x^2+4x) is (-7x^2+10x+20)/((x^2+4x)^2)