What is the derivative of f(x)=(5x)/(7x^2+1) ?

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

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

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

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derivative of

f (x) = \frac{5 x}{7 x ^{2} + 1}

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

Solution steps

\frac{d}{d x} (\frac{5 x}{7 x ^{2} + 1})

Take the constant out:

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

= 5 \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}}

= 5 \cdot \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

= 5 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}} : \frac{5 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

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

x \to - 2.4 lim ([x])

y = \frac{4}{1 + x ^{2}}, (1, 2)

\int \frac{6 - 2 x}{9 - x ^{2}} d x

\int \frac{5 x - 6}{x ^{2} + 4} d x

\frac{\partial}{\partial x} (sin (7 x^{4} y - 7 x y^{4}))

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