What is the derivative of f(x)=((x-2)(3+5x))/(x^2+1) ?

The derivative of f(x)=((x-2)(3+5x))/(x^2+1) is (7x^2+22x-7)/((x^2+1)^2)

What is the first derivative of f(x)=((x-2)(3+5x))/(x^2+1) ?

The first derivative of f(x)=((x-2)(3+5x))/(x^2+1) is (7x^2+22x-7)/((x^2+1)^2)

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derivative of

f (x) = \frac{( x - 2 ) ( 3 + 5 x )}{x ^{2} + 1}

\frac{7 x ^{2} + 22 x - 7}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x - 2 ) ( 3 + 5 x )}{x ^{2} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( x - 2 ) ( 3 + 5 x ) ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( x - 2 ) ( 3 + 5 x )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} ((x - 2) (3 + 5 x)) = 10 x - 7

\frac{d}{d x} (x^{2} + 1) = 2 x

= \frac{( 10 x - 7 ) ( x ^{2} + 1 ) - 2 x ( x - 2 ) ( 3 + 5 x )}{( x ^{2} + 1 ) ^{2}}

Expand

(10 x - 7) (x^{2} + 1) - 2 x (x - 2) (3 + 5 x) : 7 x^{2} + 22 x - 7

= \frac{7 x ^{2} + 22 x - 7}{( x ^{2} + 1 ) ^{2}}

\int \frac{4}{e ^{2 x}} d x

\int \frac{( 1 - 3 x )}{( 3 + 2 x )} d x

\frac{y ^{^{'}} + y ^{2}}{x ^{2}} = 0

\frac{d}{d M} (M^{2} (\frac{C}{2} - \frac{M}{3}))

x \to 0 lim (e^{1 - \frac{1}{x}})

What is the derivative of f(x)=((x-2)(3+5x))/(x^2+1) ?
The derivative of f(x)=((x-2)(3+5x))/(x^2+1) is (7x^2+22x-7)/((x^2+1)^2)
What is the first derivative of f(x)=((x-2)(3+5x))/(x^2+1) ?
The first derivative of f(x)=((x-2)(3+5x))/(x^2+1) is (7x^2+22x-7)/((x^2+1)^2)