What is the derivative of (5x/(9x^2+1)) ?

The derivative of (5x/(9x^2+1)) is (5(-9x^2+1))/((9x^2+1)^2)

What is the first derivative of (5x/(9x^2+1)) ?

The first derivative of (5x/(9x^2+1)) is (5(-9x^2+1))/((9x^2+1)^2)

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\frac{d}{d x} (\frac{5 x}{9 x ^{2} + 1})

\frac{5 ( - 9 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x}{9 x ^{2} + 1})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{x}{9 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} ( 9 x ^{2} + 1 ) - \frac{d}{d x} ( 9 x ^{2} + 1 ) x}{( 9 x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (9 x^{2} + 1) = 18 x

= 5 \cdot \frac{1 \cdot ( 9 x ^{2} + 1 ) - 18 xx}{( 9 x ^{2} + 1 ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( 9 x ^{2} + 1 ) - 18 xx}{( 9 x ^{2} + 1 ) ^{2}} : \frac{5 ( - 9 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ^{2}}

= \frac{5 ( - 9 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ^{2}}

y^{^{'}} = y - k

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

(- 7, - 7), (- 3, 6)

\int \frac{cos ^{4} ( x )}{sin ^{6} ( x )} d x

\int - 7 csc^{2} (x) d x

What is the derivative of (5x/(9x^2+1)) ?
The derivative of (5x/(9x^2+1)) is (5(-9x^2+1))/((9x^2+1)^2)
What is the first derivative of (5x/(9x^2+1)) ?
The first derivative of (5x/(9x^2+1)) is (5(-9x^2+1))/((9x^2+1)^2)