What is the derivative of p(t)=25e^{0.03t} ?

The derivative of p(t)=25e^{0.03t} is 0.75e^{0.03t}

What is the first derivative of p(t)=25e^{0.03t} ?

The first derivative of p(t)=25e^{0.03t} is 0.75e^{0.03t}

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derivative of

p (t) = 25 e^{0.03 t}

0.75 e^{0.03 t}

Solution steps

\frac{d}{d t} (25 e^{0.03 t})

Take the constant out:

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

= 25 \frac{d}{d t} (e^{0.03 t})

Apply the chain rule:

e^{0.03 t} \frac{d}{d t} (0.03 t)

= e^{0.03 t} \frac{d}{d t} (0.03 t)

\frac{d}{d t} (0.03 t) = 0.03

= 25 e^{0.03 t} \cdot 0.03

Simplify

= 0.75 e^{0.03 t}

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What is the derivative of p(t)=25e^{0.03t} ?
The derivative of p(t)=25e^{0.03t} is 0.75e^{0.03t}
What is the first derivative of p(t)=25e^{0.03t} ?
The first derivative of p(t)=25e^{0.03t} is 0.75e^{0.03t}