What is the derivative of (2x-5^4(8x^2-5)^{-3}) ?

The derivative of (2x-5^4(8x^2-5)^{-3}) is (8(2x-5)^3)/((8x^2-5)^3)-(48x(2x-5)^4)/((8x^2-5)^4)

What is the first derivative of (2x-5^4(8x^2-5)^{-3}) ?

The first derivative of (2x-5^4(8x^2-5)^{-3}) is (8(2x-5)^3)/((8x^2-5)^3)-(48x(2x-5)^4)/((8x^2-5)^4)

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\frac{d}{d x} ((2 x - 5)^{4} (8 x^{2} - 5)^{- 3})

\frac{8 ( 2 x - 5 ) ^{3}}{( 8 x ^{2} - 5 ) ^{3}} - \frac{48 x ( 2 x - 5 ) ^{4}}{( 8 x ^{2} - 5 ) ^{4}}

Solution steps

\frac{d}{d x} ((2 x - 5)^{4} (8 x^{2} - 5)^{- 3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (2 x - 5)^{4}, g = (8 x^{2} - 5)^{- 3}

= \frac{d}{d x} ((2 x - 5)^{4}) (8 x^{2} - 5)^{- 3} + \frac{d}{d x} ((8 x^{2} - 5)^{- 3}) (2 x - 5)^{4}

\frac{d}{d x} ((2 x - 5)^{4}) = 8 (2 x - 5)^{3}

\frac{d}{d x} ((8 x^{2} - 5)^{- 3}) = - \frac{48 x}{( 8 x ^{2} - 5 ) ^{4}}

= 8 (2 x - 5)^{3} (8 x^{2} - 5)^{- 3} + (- \frac{48 x}{( 8 x ^{2} - 5 ) ^{4}}) (2 x - 5)^{4}

Simplify

8 (2 x - 5)^{3} (8 x^{2} - 5)^{- 3} + (- \frac{48 x}{( 8 x ^{2} - 5 ) ^{4}}) (2 x - 5)^{4} : \frac{8 ( 2 x - 5 ) ^{3}}{( 8 x ^{2} - 5 ) ^{3}} - \frac{48 x ( 2 x - 5 ) ^{4}}{( 8 x ^{2} - 5 ) ^{4}}

= \frac{8 ( 2 x - 5 ) ^{3}}{( 8 x ^{2} - 5 ) ^{3}} - \frac{48 x ( 2 x - 5 ) ^{4}}{( 8 x ^{2} - 5 ) ^{4}}

\frac{\partial}{\partial u} (\frac{uv}{v + 1})

\frac{d}{d x} (x^{3} - 6 x^{2} + 9 x - 4)

\int (x + 1) (x^{2} + 2 x) d x

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

x \to - 3 lim (\frac{2}{x ^{2} - 9})

What is the derivative of (2x-5^4(8x^2-5)^{-3}) ?
The derivative of (2x-5^4(8x^2-5)^{-3}) is (8(2x-5)^3)/((8x^2-5)^3)-(48x(2x-5)^4)/((8x^2-5)^4)
What is the first derivative of (2x-5^4(8x^2-5)^{-3}) ?
The first derivative of (2x-5^4(8x^2-5)^{-3}) is (8(2x-5)^3)/((8x^2-5)^3)-(48x(2x-5)^4)/((8x^2-5)^4)