What is the derivative of 5000(1-1/40 t)^2 ?

The derivative of 5000(1-1/40 t)^2 is -250(1-t/(40))

What is the first derivative of 5000(1-1/40 t)^2 ?

The first derivative of 5000(1-1/40 t)^2 is -250(1-t/(40))

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derivative of

5000 (1 - \frac{1}{40} t)^{2}

- 250 (1 - \frac{t}{40})

Solution steps

\frac{d}{d t} (5000 (1 - \frac{1}{40} t)^{2})

Simplify

5000 (1 - \frac{1}{40} t)^{2} : 5000 (1 - \frac{t}{40})^{2}

= \frac{d}{d t} (5000 (1 - \frac{t}{40})^{2})

Take the constant out:

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

= 5000 \frac{d}{d t} ((1 - \frac{t}{40})^{2})

Apply the chain rule:

2 (1 - \frac{t}{40}) \frac{d}{d t} (1 - \frac{t}{40})

= 2 (1 - \frac{t}{40}) \frac{d}{d t} (1 - \frac{t}{40})

\frac{d}{d t} (1 - \frac{t}{40}) = - \frac{1}{40}

= 5000 \cdot 2 (1 - \frac{t}{40}) (- \frac{1}{40})

Simplify

5000 \cdot 2 (1 - \frac{t}{40}) (- \frac{1}{40}) : - 250 (1 - \frac{t}{40})

= - 250 (1 - \frac{t}{40})

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What is the derivative of 5000(1-1/40 t)^2 ?
The derivative of 5000(1-1/40 t)^2 is -250(1-t/(40))
What is the first derivative of 5000(1-1/40 t)^2 ?
The first derivative of 5000(1-1/40 t)^2 is -250(1-t/(40))