What is the derivative of f(x)=1680(2x+5)^4 ?

The derivative of f(x)=1680(2x+5)^4 is 13440(2x+5)^3

What is the first derivative of f(x)=1680(2x+5)^4 ?

The first derivative of f(x)=1680(2x+5)^4 is 13440(2x+5)^3

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derivative of

f (x) = 1680 (2 x + 5)^{4}

13440 (2 x + 5)^{3}

Solution steps

\frac{d}{d x} (1680 (2 x + 5)^{4})

Take the constant out:

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

= 1680 \frac{d}{d x} ((2 x + 5)^{4})

Apply the chain rule:

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

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

\frac{d}{d x} (2 x + 5) = 2

= 1680 \cdot 4 (2 x + 5)^{3} \cdot 2

Simplify

= 13440 (2 x + 5)^{3}

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What is the derivative of f(x)=1680(2x+5)^4 ?
The derivative of f(x)=1680(2x+5)^4 is 13440(2x+5)^3
What is the first derivative of f(x)=1680(2x+5)^4 ?
The first derivative of f(x)=1680(2x+5)^4 is 13440(2x+5)^3