en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=csc^1(e^{8t})

Solution

derivative of

y = csc^{1} (e^{8 t})

Solution

- cot (e^{8 t}) csc (e^{8 t}) e^{8 t} \cdot 8

Solution steps

\frac{d}{d t} (csc^{1} (e^{8 t}))

Simplify

csc^{1} (e^{8 t}) : csc (e^{8 t})

= \frac{d}{d t} (csc (e^{8 t}))

Apply the chain rule:

- cot (e^{8 t}) csc (e^{8 t}) \frac{d}{d t} (e^{8 t})

= - cot (e^{8 t}) csc (e^{8 t}) \frac{d}{d t} (e^{8 t})

\frac{d}{d t} (e^{8 t}) = e^{8 t} \cdot 8

= - cot (e^{8 t}) csc (e^{8 t}) e^{8 t} \cdot 8

Popular Examples

integral of (x^3-7x)

\int (x^{3} - 7 x) d x

(\partial)/(\partial x)(ln(x^2u))

\frac{\partial}{\partial x} (ln (x^{2} u))

derivative of f(x)=(2x+3)^6(x-2)^4 derivative of

f (x) = (2 x + 3)^{6} (x - 2)^{4}

integral of x+pi

\int x + π d x

derivative of f(x)=sqrt(7x+8)derivative of

f (x) = 7 x + 8

Frequently Asked Questions (FAQ)

What is the derivative of y=csc^1(e^{8t}) ?
The derivative of y=csc^1(e^{8t}) is -cot(e^{8t})csc(e^{8t})e^{8t}*8
What is the first derivative of y=csc^1(e^{8t}) ?
The first derivative of y=csc^1(e^{8t}) is -cot(e^{8t})csc(e^{8t})e^{8t}*8