What is the derivative of (6x^5-7x/(x^4-8)) ?

The derivative of (6x^5-7x/(x^4-8)) is (6x^8-219x^4+56)/((x^4-8)^2)

What is the first derivative of (6x^5-7x/(x^4-8)) ?

The first derivative of (6x^5-7x/(x^4-8)) is (6x^8-219x^4+56)/((x^4-8)^2)

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\frac{d}{d x} (\frac{6 x ^{5} - 7 x}{x ^{4} - 8})

\frac{6 x ^{8} - 219 x ^{4} + 56}{( x ^{4} - 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x ^{5} - 7 x}{x ^{4} - 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x ^{5} - 7 x ) ( x ^{4} - 8 ) - \frac{d}{d x} ( x ^{4} - 8 ) ( 6 x ^{5} - 7 x )}{( x ^{4} - 8 ) ^{2}}

\frac{d}{d x} (6 x^{5} - 7 x) = 30 x^{4} - 7

\frac{d}{d x} (x^{4} - 8) = 4 x^{3}

= \frac{( 30 x ^{4} - 7 ) ( x ^{4} - 8 ) - 4 x ^{3} ( 6 x ^{5} - 7 x )}{( x ^{4} - 8 ) ^{2}}

Expand

(30 x^{4} - 7) (x^{4} - 8) - 4 x^{3} (6 x^{5} - 7 x) : 6 x^{8} - 219 x^{4} + 56

= \frac{6 x ^{8} - 219 x ^{4} + 56}{( x ^{4} - 8 ) ^{2}}

\int (6 e^{- 0.2 x}) d x

5 - x, 25 - x^{2}

\int \frac{1}{x ^{2}} arctan (x) d x

x \to 4 + lim (x - 4)

f (x) = 0.6 x^{1.5}

What is the derivative of (6x^5-7x/(x^4-8)) ?
The derivative of (6x^5-7x/(x^4-8)) is (6x^8-219x^4+56)/((x^4-8)^2)
What is the first derivative of (6x^5-7x/(x^4-8)) ?
The first derivative of (6x^5-7x/(x^4-8)) is (6x^8-219x^4+56)/((x^4-8)^2)