What is the derivative of ((6x^9+x^8))/(2x^4) ?

The derivative of ((6x^9+x^8))/(2x^4) is x^3(15x+2)

What is the first derivative of ((6x^9+x^8))/(2x^4) ?

The first derivative of ((6x^9+x^8))/(2x^4) is x^3(15x+2)

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derivative of

\frac{( 6 x ^{9} + x ^{8} )}{2 x ^{4}}

x^{3} (15 x + 2)

Solution steps

\frac{d}{d x} (\frac{6 x ^{9} + x ^{8}}{2 x ^{4}})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{6 x ^{9} + x ^{8}}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 6 x ^{9} + x ^{8} ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 6 x ^{9} + x ^{8} )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (6 x^{9} + x^{8}) = 54 x^{8} + 8 x^{7}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{2} \cdot \frac{( 54 x ^{8} + 8 x ^{7} ) x ^{4} - 4 x ^{3} ( 6 x ^{9} + x ^{8} )}{( x ^{4} ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( 54 x ^{8} + 8 x ^{7} ) x ^{4} - 4 x ^{3} ( 6 x ^{9} + x ^{8} )}{( x ^{4} ) ^{2}} : x^{3} (15 x + 2)

= x^{3} (15 x + 2)

\frac{\partial}{\partial x} (y + 2 x)

\int_{1}^{3} 3 x^{- \frac{3}{2}} d x

\int (5 x^{4} + 12 x^{3} + 6 x - 2) d x

(2 y + 2 t - 3) d t + (8 y + 2 t - 1) d y = 0

\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3}

What is the derivative of ((6x^9+x^8))/(2x^4) ?
The derivative of ((6x^9+x^8))/(2x^4) is x^3(15x+2)
What is the first derivative of ((6x^9+x^8))/(2x^4) ?
The first derivative of ((6x^9+x^8))/(2x^4) is x^3(15x+2)