en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(sec(t)tan(t))

Solution

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

Solution

- sec (t) + 2 sec^{3} (t)

Solution steps

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

Apply the Product Rule:

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

f = sec (t), g = tan (t)

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

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

\frac{d}{d t} (tan (t)) = sec^{2} (t)

= sec (t) tan (t) tan (t) + sec^{2} (t) sec (t)

Simplify

sec (t) tan (t) tan (t) + sec^{2} (t) sec (t) : - sec (t) + 2 sec^{3} (t)

= - sec (t) + 2 sec^{3} (t)

Popular Examples

derivative of-2cot(x+3csc(x))

\frac{d}{d x} (- 2 cot (x) + 3 csc (x))

area y=5cos(x),y=5sin(x),0<= x<= pi area

y = 5 cos (x), y = 5 sin (x), 0 \leq x \leq π

derivative of (x^2-1^{1/3})

\frac{d}{d x} ((x^{2} - 1)^{\frac{1}{3}})

integral of 0sin(nx)

\int 0 sin (n x) d x

f(x)=0.1x^3-0.45x^2+2.43x+300

f (x) = 0.1 x^{3} - 0.45 x^{2} + 2.43 x + 300

Frequently Asked Questions (FAQ)

What is the d/(dt)(sec(t)tan(t)) ?
The d/(dt)(sec(t)tan(t)) is -sec(t)+2sec^3(t)
What is the first d/(dt)(sec(t)tan(t)) ?
The first d/(dt)(sec(t)tan(t)) is -sec(t)+2sec^3(t)