What is the derivative of ((7x^2-8^4)/x) ?

The derivative of ((7x^2-8^4)/x) is (56x^2(7x^2-8)^3-(7x^2-8)^4)/(x^2)

What is the first derivative of ((7x^2-8^4)/x) ?

The first derivative of ((7x^2-8^4)/x) is (56x^2(7x^2-8)^3-(7x^2-8)^4)/(x^2)

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

\frac{56 x ^{2} ( 7 x ^{2} - 8 ) ^{3} - ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((7 x^{2} - 8)^{4}) = 56 x (7 x^{2} - 8)^{3}

\frac{d x}{d x} = 1

= \frac{56 x ( 7 x ^{2} - 8 ) ^{3} x - 1 \cdot ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}

56 x (7 x^{2} - 8)^{3} x - 1 \cdot (7 x^{2} - 8)^{4} = 56 x^{2} (7 x^{2} - 8)^{3} - (7 x^{2} - 8)^{4}

= \frac{56 x ^{2} ( 7 x ^{2} - 8 ) ^{3} - ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}

t a y l or e^{x} cos (x)

\int 6 e^{2} d x

\int_{- 8}^{27} \frac{1}{3 x} d x

l a pl a ce t r an s f or m e^{- 5 t} sin (2 t)

(2 x y - sec^{2} (x)) d x + (x^{2} + 2 y) d y = 0

What is the derivative of ((7x^2-8^4)/x) ?
The derivative of ((7x^2-8^4)/x) is (56x^2(7x^2-8)^3-(7x^2-8)^4)/(x^2)
What is the first derivative of ((7x^2-8^4)/x) ?
The first derivative of ((7x^2-8^4)/x) is (56x^2(7x^2-8)^3-(7x^2-8)^4)/(x^2)