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

The derivative of (7x/(sqrt(x^2+5))) is (35)/((x^2+5)sqrt(x^2+5))

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

The first derivative of (7x/(sqrt(x^2+5))) is (35)/((x^2+5)sqrt(x^2+5))

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

\frac{35}{( x ^{2} + 5 ) x ^{2} + 5}

Solution steps

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

Take the constant out:

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

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

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

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

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

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

Simplify

7 \cdot \frac{1 \cdot x ^{2} + 5 - \frac{x}{x ^{2} + 5} x}{( x ^{2} + 5 ) ^{2}} : \frac{35}{( x ^{2} + 5 ) x ^{2} + 5}

= \frac{35}{( x ^{2} + 5 ) x ^{2} + 5}

\int e^{x} sin (2 x) d x

\int \frac{x ( x - 2 ) ^{2}}{x ^{4} + 1} d x

\int \frac{cos ^{2} ( x )}{cos ( x )} d x

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

(- 4, 1), (- 7, - 5)

What is the derivative of (7x/(sqrt(x^2+5))) ?
The derivative of (7x/(sqrt(x^2+5))) is (35)/((x^2+5)sqrt(x^2+5))
What is the first derivative of (7x/(sqrt(x^2+5))) ?
The first derivative of (7x/(sqrt(x^2+5))) is (35)/((x^2+5)sqrt(x^2+5))