What is the derivative of (4sqrt(5x^3+x)/((x-1))) ?

The derivative of (4sqrt(5x^3+x)/((x-1))) is (2(5x^3-15x^2-x-1))/((x-1)^2sqrt(5x^3+x))

What is the first derivative of (4sqrt(5x^3+x)/((x-1))) ?

The first derivative of (4sqrt(5x^3+x)/((x-1))) is (2(5x^3-15x^2-x-1))/((x-1)^2sqrt(5x^3+x))

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\frac{d}{d x} (\frac{4 5 x ^{3} + x}{( x - 1 )})

\frac{2 ( 5 x ^{3} - 15 x ^{2} - x - 1 )}{( x - 1 ) ^{2} 5 x ^{3} + x}

Solution steps

\frac{d}{d x} (\frac{4 5 x ^{3} + x}{( x - 1 )})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x^{3} + x) = \frac{15 x ^{2} + 1}{2 5 x ^{3} + x}

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

= 4 \cdot \frac{\frac{15 x ^{2} + 1}{2 5 x ^{3} + x} ( x - 1 ) - 1 \cdot 5 x ^{3} + x}{( x - 1 ) ^{2}}

Simplify

4 \cdot \frac{\frac{15 x ^{2} + 1}{2 5 x ^{3} + x} ( x - 1 ) - 1 \cdot 5 x ^{3} + x}{( x - 1 ) ^{2}} : \frac{2 ( 5 x ^{3} - 15 x ^{2} - x - 1 )}{( x - 1 ) ^{2} 5 x ^{3} + x}

= \frac{2 ( 5 x ^{3} - 15 x ^{2} - x - 1 )}{( x - 1 ) ^{2} 5 x ^{3} + x}

\frac{0.1 \cdot m}{s + 0.1 \cdot m}

\frac{x}{x + 4}

\frac{1}{s + 1} - s - 1

y = x^{5}, (- 1, - 1)

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

What is the derivative of (4sqrt(5x^3+x)/((x-1))) ?
The derivative of (4sqrt(5x^3+x)/((x-1))) is (2(5x^3-15x^2-x-1))/((x-1)^2sqrt(5x^3+x))
What is the first derivative of (4sqrt(5x^3+x)/((x-1))) ?
The first derivative of (4sqrt(5x^3+x)/((x-1))) is (2(5x^3-15x^2-x-1))/((x-1)^2sqrt(5x^3+x))