What is the derivative of (5x^6+4x^5+3x^4/(6x^2)) ?

The derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3

What is the first derivative of (5x^6+4x^5+3x^4/(6x^2)) ?

The first derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3

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\frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{6 x ^{2}})

\frac{x ( 10 x ^{2} + 6 x + 3 )}{3}

Solution steps

\frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{6 x ^{2}})

Take the constant out:

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

= \frac{1}{6} \frac{d}{d x} (\frac{5 x ^{6} + 4 x ^{5} + 3 x ^{4}}{x ^{2}})

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} ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (5 x^{6} + 4 x^{5} + 3 x^{4}) = 30 x^{5} + 20 x^{4} + 12 x^{3}

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

= \frac{1}{6} \cdot \frac{( 30 x ^{5} + 20 x ^{4} + 12 x ^{3} ) x ^{2} - 2 x ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{6} \cdot \frac{( 30 x ^{5} + 20 x ^{4} + 12 x ^{3} ) x ^{2} - 2 x ( 5 x ^{6} + 4 x ^{5} + 3 x ^{4} )}{( x ^{2} ) ^{2}} : \frac{x ( 10 x ^{2} + 6 x + 3 )}{3}

= \frac{x ( 10 x ^{2} + 6 x + 3 )}{3}

What is the derivative of (5x^6+4x^5+3x^4/(6x^2)) ?
The derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3
What is the first derivative of (5x^6+4x^5+3x^4/(6x^2)) ?
The first derivative of (5x^6+4x^5+3x^4/(6x^2)) is (x(10x^2+6x+3))/3