What is the derivative of (7x/(x^2+49)) ?

The derivative of (7x/(x^2+49)) is (7(-x^2+49))/((x^2+49)^2)

What is the first derivative of (7x/(x^2+49)) ?

The first derivative of (7x/(x^2+49)) is (7(-x^2+49))/((x^2+49)^2)

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\frac{d}{d x} (\frac{7 x}{x ^{2} + 49})

\frac{7 ( - x ^{2} + 49 )}{( x ^{2} + 49 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x}{x ^{2} + 49})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{x}{x ^{2} + 49})

Apply the Quotient Rule:

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

= 7 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 49 ) - \frac{d}{d x} ( x ^{2} + 49 ) x}{( x ^{2} + 49 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 49) = 2 x

= 7 \cdot \frac{1 \cdot ( x ^{2} + 49 ) - 2 xx}{( x ^{2} + 49 ) ^{2}}

Simplify

7 \cdot \frac{1 \cdot ( x ^{2} + 49 ) - 2 xx}{( x ^{2} + 49 ) ^{2}} : \frac{7 ( - x ^{2} + 49 )}{( x ^{2} + 49 ) ^{2}}

= \frac{7 ( - x ^{2} + 49 )}{( x ^{2} + 49 ) ^{2}}

\frac{d ^{4}}{d x ^{4}} (4 e^{x^{2}})

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

\frac{\partial}{\partial x} (y^{2} ln (x))

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

\frac{d}{d x} (e^{2} (sin (\frac{π}{4}) - 1))

What is the derivative of (7x/(x^2+49)) ?
The derivative of (7x/(x^2+49)) is (7(-x^2+49))/((x^2+49)^2)
What is the first derivative of (7x/(x^2+49)) ?
The first derivative of (7x/(x^2+49)) is (7(-x^2+49))/((x^2+49)^2)