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

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

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

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

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\frac{d}{d 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}}

y^{^{''}} + a y = 0

n = 1 \sum \infty n^{2}

\int_{- 8}^{8} 64 - x^{2} d x

\frac{d y}{d x} = 3 - 6 x + y - 2 x y

(1 + x) cos (x)

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