What is the derivative of (4x/(sqrt(x^2+7))) ?

The derivative of (4x/(sqrt(x^2+7))) is (28)/((x^2+7)sqrt(x^2+7))

What is the first derivative of (4x/(sqrt(x^2+7))) ?

The first derivative of (4x/(sqrt(x^2+7))) is (28)/((x^2+7)sqrt(x^2+7))

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\frac{d}{d x} (\frac{4 x}{x ^{2} + 7})

\frac{28}{( x ^{2} + 7 ) x ^{2} + 7}

Solution steps

\frac{d}{d x} (\frac{4 x}{x ^{2} + 7})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{x}{x ^{2} + 7})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} x ^{2} + 7 - \frac{d}{d x} ( x ^{2} + 7 ) x}{( x ^{2} + 7 ) ^{2}}

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

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

= 4 \cdot \frac{1 \cdot x ^{2} + 7 - \frac{x}{x ^{2} + 7} x}{( x ^{2} + 7 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot x ^{2} + 7 - \frac{x}{x ^{2} + 7} x}{( x ^{2} + 7 ) ^{2}} : \frac{28}{( x ^{2} + 7 ) x ^{2} + 7}

= \frac{28}{( x ^{2} + 7 ) x ^{2} + 7}

\int x^{\frac{3}{2}} d x

\int_{1}^{e} ln (14 x) d x

\int \frac{cos ^{4} ( x )}{sin ^{2} ( x )} d x

\frac{( s ^{2} )}{s ^{3} - 1}

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2})})

What is the derivative of (4x/(sqrt(x^2+7))) ?
The derivative of (4x/(sqrt(x^2+7))) is (28)/((x^2+7)sqrt(x^2+7))
What is the first derivative of (4x/(sqrt(x^2+7))) ?
The first derivative of (4x/(sqrt(x^2+7))) is (28)/((x^2+7)sqrt(x^2+7))