What is the derivative of (7x^3+x/(6sqrt(x))) ?

The derivative of (7x^3+x/(6sqrt(x))) is (35x^2+1)/(12sqrt(x))

What is the first derivative of (7x^3+x/(6sqrt(x))) ?

The first derivative of (7x^3+x/(6sqrt(x))) is (35x^2+1)/(12sqrt(x))

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\frac{d}{d x} (\frac{7 x ^{3} + x}{6 x})

\frac{35 x ^{2} + 1}{12 x}

Solution steps

\frac{d}{d x} (\frac{7 x ^{3} + x}{6 x})

Take the constant out:

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

= \frac{1}{6} \frac{d}{d x} (\frac{7 x ^{3} + x}{x})

Apply the Quotient Rule:

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

= \frac{1}{6} \cdot \frac{\frac{d}{d x} ( 7 x ^{3} + x ) x - \frac{d}{d x} ( x ) ( 7 x ^{3} + x )}{( x ) ^{2}}

\frac{d}{d x} (7 x^{3} + x) = 21 x^{2} + 1

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{1}{6} \cdot \frac{( 21 x ^{2} + 1 ) x - \frac{1}{2 x} ( 7 x ^{3} + x )}{( x ) ^{2}}

Simplify

\frac{1}{6} \cdot \frac{( 21 x ^{2} + 1 ) x - \frac{1}{2 x} ( 7 x ^{3} + x )}{( x ) ^{2}} : \frac{35 x ^{2} + 1}{12 x}

= \frac{35 x ^{2} + 1}{12 x}

What is the derivative of (7x^3+x/(6sqrt(x))) ?
The derivative of (7x^3+x/(6sqrt(x))) is (35x^2+1)/(12sqrt(x))
What is the first derivative of (7x^3+x/(6sqrt(x))) ?
The first derivative of (7x^3+x/(6sqrt(x))) is (35x^2+1)/(12sqrt(x))