What is the derivative of f(x)= x/(7x^2+1) ?

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

What is the first derivative of f(x)= x/(7x^2+1) ?

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}}

1 \cdot (7 x^{2} + 1) - 14 xx = - 7 x^{2} + 1

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

\frac{x + 1}{x ^{3} + x - 2}

\frac{d y}{d t} = - \frac{1}{5} y

\int_{π}^{5 π} x^{2} sin (x) d x

8 w^{4} + 3 w^{2} + 7 w

\int (x^{2} - 4 x + 4)^{\frac{4}{3}} d x

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