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Popular >

derivative of 3tsec(t)

Solution

derivative of

3 t sec (t)

Solution

3 (sec (t) + t sec (t) tan (t))

Solution steps

\frac{d}{d t} (3 t sec (t))

Take the constant out:

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

= 3 \frac{d}{d t} (t sec (t))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = sec (t)

= 3 (\frac{d t}{d t} sec (t) + \frac{d}{d t} (sec (t)) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (sec (t)) = sec (t) tan (t)

= 3 (1 \cdot sec (t) + sec (t) tan (t) t)

Simplify

= 3 (sec (t) + t sec (t) tan (t))

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Frequently Asked Questions (FAQ)

What is the derivative of 3tsec(t) ?
The derivative of 3tsec(t) is 3(sec(t)+tsec(t)tan(t))
What is the first derivative of 3tsec(t) ?
The first derivative of 3tsec(t) is 3(sec(t)+tsec(t)tan(t))