What is the derivative of (8x-7^{-5}) ?

The derivative of (8x-7^{-5}) is -(40)/((8x-7)^6)

What is the first derivative of (8x-7^{-5}) ?

The first derivative of (8x-7^{-5}) is -(40)/((8x-7)^6)

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

- \frac{40}{( 8 x - 7 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

= - \frac{5}{( 8 x - 7 ) ^{6}} \cdot 8

Simplify

- \frac{5}{( 8 x - 7 ) ^{6}} \cdot 8 : - \frac{40}{( 8 x - 7 ) ^{6}}

= - \frac{40}{( 8 x - 7 ) ^{6}}

x \to 0 lim (1 + x - 1)

y \to 0 lim (\frac{sin ( 5 y )}{7 y})

\int x lo g_{e} (x) d x

x \to 0 lim (sin^{x} (x))

\frac{d}{d x} (cos (x^{2} - 2 x))

What is the derivative of (8x-7^{-5}) ?
The derivative of (8x-7^{-5}) is -(40)/((8x-7)^6)
What is the first derivative of (8x-7^{-5}) ?
The first derivative of (8x-7^{-5}) is -(40)/((8x-7)^6)