What is the derivative of 7(4x^2-7x+2)^{-6} ?

The derivative of 7(4x^2-7x+2)^{-6} is -(42(8x-7))/((4x^2-7x+2)^7)

What is the first derivative of 7(4x^2-7x+2)^{-6} ?

The first derivative of 7(4x^2-7x+2)^{-6} is -(42(8x-7))/((4x^2-7x+2)^7)

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derivative of

7 (4 x^{2} - 7 x + 2)^{- 6}

- \frac{42 ( 8 x - 7 )}{( 4 x ^{2} - 7 x + 2 ) ^{7}}

Solution steps

\frac{d}{d x} (7 (4 x^{2} - 7 x + 2)^{- 6})

Take the constant out:

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

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

Apply the chain rule:

- \frac{6}{( 4 x ^{2} - 7 x + 2 ) ^{7}} \frac{d}{d x} (4 x^{2} - 7 x + 2)

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

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

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

Simplify

7 (- \frac{6}{( 4 x ^{2} - 7 x + 2 ) ^{7}} (8 x - 7)) : - \frac{42 ( 8 x - 7 )}{( 4 x ^{2} - 7 x + 2 ) ^{7}}

= - \frac{42 ( 8 x - 7 )}{( 4 x ^{2} - 7 x + 2 ) ^{7}}

x \to \infty lim (x^{2} + 5)

x \to 2 - lim (\frac{x - 1}{x - 2})

x \to \frac{π}{2} lim (cos^{c o s (x)} (x))

t e^{2 t}

\frac{( x + 1 )}{( x + 7 )}

What is the derivative of 7(4x^2-7x+2)^{-6} ?
The derivative of 7(4x^2-7x+2)^{-6} is -(42(8x-7))/((4x^2-7x+2)^7)
What is the first derivative of 7(4x^2-7x+2)^{-6} ?
The first derivative of 7(4x^2-7x+2)^{-6} is -(42(8x-7))/((4x^2-7x+2)^7)