en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

d/(dt)(cot^4(t)-csc^4(t))

Solution

\frac{d}{d t} (cot^{4} (t) - csc^{4} (t))

Solution

4 csc^{2} (t) cot (t)

Solution steps

\frac{d}{d t} (cot^{4} (t) - csc^{4} (t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (cot^{4} (t)) - \frac{d}{d t} (csc^{4} (t))

\frac{d}{d t} (cot^{4} (t)) = - 4 cot^{3} (t) csc^{2} (t)

\frac{d}{d t} (csc^{4} (t)) = - 4 csc^{4} (t) cot (t)

= - 4 cot^{3} (t) csc^{2} (t) - (- 4 csc^{4} (t) cot (t))

Simplify

- 4 cot^{3} (t) csc^{2} (t) - (- 4 csc^{4} (t) cot (t)) : 4 csc^{2} (t) cot (t)

= 4 csc^{2} (t) cot (t)

Graph

Popular Examples

limit as x approaches 4 of 8-2x

x \to 4 lim (8 - 2 x)

limit as x approaches infinity of 8^x

x \to \infty lim (8^{x})

integral of 8x^2e^x

\int 8 x^{2} e^{x} d x

derivative of 2(x+4)^{3/2}derivative of

2 (x + 4)^{\frac{3}{2}}

(\partial)/(\partial x)(y^2+x^2-4x-3)

\frac{\partial}{\partial x} (y^{2} + x^{2} - 4 x - 3)

Frequently Asked Questions (FAQ)

What is the d/(dt)(cot^4(t)-csc^4(t)) ?
The d/(dt)(cot^4(t)-csc^4(t)) is 4csc^2(t)cot(t)
What is the first d/(dt)(cot^4(t)-csc^4(t)) ?
The first d/(dt)(cot^4(t)-csc^4(t)) is 4csc^2(t)cot(t)