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

The derivative of 4(5-7x)^5 is -140(5-7x)^4

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

The first derivative of 4(5-7x)^5 is -140(5-7x)^4

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derivative of

4 (5 - 7 x)^{5}

- 140 (5 - 7 x)^{4}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 4 \cdot 5 (5 - 7 x)^{4} (- 7)

Simplify

= - 140 (5 - 7 x)^{4}

What is the derivative of 4(5-7x)^5 ?
The derivative of 4(5-7x)^5 is -140(5-7x)^4
What is the first derivative of 4(5-7x)^5 ?
The first derivative of 4(5-7x)^5 is -140(5-7x)^4