What is the derivative of f(x)=3(5-x)^2 ?

The derivative of f(x)=3(5-x)^2 is -6(5-x)

What is the first derivative of f(x)=3(5-x)^2 ?

The first derivative of f(x)=3(5-x)^2 is -6(5-x)

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derivative of

f (x) = 3 (5 - x)^{2}

- 6 (5 - x)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

2 (5 - x) \frac{d}{d x} (5 - x)

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

\frac{d}{d x} (5 - x) = - 1

= 3 \cdot 2 (5 - x) (- 1)

Simplify

= - 6 (5 - x)

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What is the derivative of f(x)=3(5-x)^2 ?
The derivative of f(x)=3(5-x)^2 is -6(5-x)
What is the first derivative of f(x)=3(5-x)^2 ?
The first derivative of f(x)=3(5-x)^2 is -6(5-x)